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  • V. Kac and P. Cheung (2002)
    Quantum Calculus,
    Universitext, Springer-Verlag, New York.
    Show Annotations
    External Links:
    ISBN 0-387-95341-8, MathReview (P. D. F. Ion), ZentralBlatt.
    Referenced by:
    Ch.17.
    Encodings:
    BibTeX
  • K. W. J. Kadell (1988)
    A proof of Askey’s conjectured q-analogue of Selberg’s integral and a conjecture of Morris,
    SIAM J. Math. Anal. 19 (4), pp. 969–986.
    Show Annotations
    External Links:
    ISSN 0036-1410, Document, MathReview (David M. Bressoud), ZentralBlatt.
    Referenced by:
    ‣ §17.13.
    Encodings:
    BibTeX
  • K. W. J. Kadell (1994)
    A proof of the q-Macdonald-Morris conjecture for BC_{n},
    Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
    Show Annotations
    External Links:
    ISSN 0065-9266, MathReview (Eric M. Opdam), ZentralBlatt.
    Referenced by:
    ‣ §17.14.
    Encodings:
    BibTeX
  • T. A. Kaeding (1995)
    Pascal program for generating tables of {\rm SU}(3) Clebsch-Gordan coefficients,
    Comput. Phys. Comm. 85 (1), pp. 82–88.
    Show Annotations
    External Links:
    ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt.
    Referenced by:
    §34.15.
    Encodings:
    BibTeX
  • W. Kahan (1987)
    Branch Cuts for Complex Elementary Functions or Much Ado About Nothing’s Sign Bit,
    in The State of the Art in Numerical Analysis (Birmingham, 1986),
    (M. J. D. Powell Ed.), Inst. Math. Appl. Conf. Ser. New Ser., Vol. 9, pp. 165–211.
    Show Annotations
    External Links:
    MathReview, ZentralBlatt.
    Referenced by:
    ‣ §4.23(iv), ‣ §4.37(iv).
    Encodings:
    BibTeX
  • D. K. Kahaner, C. Moler and S. Nash (1989)
    Numerical Methods and Software,
    Prentice Hall, Englewood Cliffs, NJ.
    Show Annotations
    Notes:
    Includes collection of single- and double-precision Fortran subroutines.
    External Links:
    ISBN 0-13-627258-4, Package NMS (in GAMS), ZentralBlatt.
    Referenced by:
    NMS (free collection of Fortran subroutines).
    Encodings:
    BibTeX
  • K. Kajiwara and T. Masuda (1999)
    On the Umemura polynomials for the Painlevé III equation,
    Phys. Lett. A 260 (6), pp. 462–467.
    Show Annotations
    External Links:
    ISSN 0375-9601, MathReview, ZentralBlatt.
    Referenced by:
    §32.8(iii).
    Encodings:
    BibTeX
  • K. Kajiwara and Y. Ohta (1996)
    Determinant structure of the rational solutions for the Painlevé II equation,
    J. Math. Phys. 37 (9), pp. 4693–4704.
    Show Annotations
    External Links:
    ISSN 0022-2488, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.
    Referenced by:
    §32.8(ii).
    Encodings:
    BibTeX
  • K. Kajiwara and Y. Ohta (1998)
    Determinant structure of the rational solutions for the Painlevé IV equation,
    J. Phys. A 31 (10), pp. 2431–2446.
    Show Annotations
    External Links:
    ISSN 0305-4470, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.
    Referenced by:
    §32.8(iv).
    Encodings:
    BibTeX
  • S. L. Kalla (1992)
    On the evaluation of the Gauss hypergeometric function,
    C. R. Acad. Bulgare Sci. 45 (6), pp. 35–36.
    Show Annotations
    External Links:
    ISSN 0861-1459, MathReview, ZentralBlatt.
    Referenced by:
    §15.15, §15.19(i).
    Encodings:
    BibTeX
  • E. G. Kalnins, W. Miller, G. F. Torres del Castillo and G. C. Williams (2000)
    Special Functions and Perturbations of Black Holes,
    in Special Functions (Hong Kong, 1999),
    pp. 140–151.
    Show Annotations
    External Links:
    MathReview, ZentralBlatt.
    Referenced by:
    §31.17(ii).
    Encodings:
    BibTeX
  • E. G. Kalnins, W. Miller and P. Winternitz (1976)
    The group {\rm{O}}(4), separation of variables and the hydrogen atom,
    SIAM J. Appl. Math. 30 (4), pp. 630–664.
    Show Annotations
    External Links:
    Document, MathReview (Anthony J. Bracken), ZentralBlatt.
    Referenced by:
    §31.17(i).
    Encodings:
    BibTeX
  • E. G. Kalnins and W. Miller (1991a)
    Hypergeometric expansions of Heun polynomials,
    SIAM J. Math. Anal. 22 (5), pp. 1450–1459.
    Show Annotations
    External Links:
    ISSN 0036-1410, Document, MathReview (Peter A. McCoy), ZentralBlatt.
    Referenced by:
    §31.16(ii).
    Encodings:
    BibTeX
  • E. G. Kalnins and W. Miller (1991b)
    Addendum: “Hypergeometric expansions of Heun polynomials”,
    SIAM J. Math. Anal. 22 (6), pp. 1803.
    Show Annotations
    External Links:
    ISSN 0036-1410, Document, MathReview (Peter A. McCoy), ZentralBlatt.
    Referenced by:
    §31.16(ii).
    Encodings:
    BibTeX
  • E. G. Kalnins and W. Miller (1993)
    Orthogonal Polynomials on n-spheres: Gegenbauer, Jacobi and Heun,
    in Topics in Polynomials of One and Several Variables and their Applications,
    pp. 299–322.
    Show Annotations
    External Links:
    MathReview, ZentralBlatt.
    Referenced by:
    §31.16(ii).
    Encodings:
    BibTeX
  • E. G. Kalnins (1986)
    Separation of Variables for Riemannian Spaces of Constant Curvature,
    Longman Scientific & Technical, Harlow.
    Show Annotations
    External Links:
    ISBN 0-582-98807-1, MathReview (H. Kilp), ZentralBlatt.
    Referenced by:
    §31.17(i).
    Encodings:
    BibTeX
  • A. Kalähne (1907)
    Über die Wurzeln einiger Zylinderfunktionen und gewisser aus ihnen gebildeter Gleichungen,
    Zeitschrift für Mathematik und Physik 54, pp. 55–86 (German).
    Show Annotations
    External Links:
    ZentralBlatt.
    Referenced by:
    §10.21(x).
    Encodings:
    BibTeX
  • J. Kamimoto (1998)
    On an integral of Hardy and Littlewood,
    Kyushu J. Math. 52 (1), pp. 249–263.
    Show Annotations
    External Links:
    ISSN 1340-6116, Document, MathReview (Fritz Haslinger), ZentralBlatt.
    Referenced by:
    §9.13(ii).
    Encodings:
    BibTeX
  • D. Kaminski and R. B. Paris (1999)
    On the zeroes of the Pearcey integral,
    J. Comput. Appl. Math. 107 (1), pp. 31–52.
    Show Annotations
    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt.
    Referenced by:
    §36.7(ii), §36.7(ii).
    Encodings:
    BibTeX
  • E. Kamke (1977)
    Differentialgleichungen: Lösungsmethoden und Lösungen. Teil I,
    B. G. Teubner, Stuttgart (German).
    Show Annotations
    External Links:
    ISBN 3-519-02017-3, MathReview, ZentralBlatt.
    Referenced by:
    §1.13(vii), §10.13, §4.20, §4.34, §4.7(ii).
    Encodings:
    BibTeX
  • M. Kaneko (1997)
    Poly-Bernoulli numbers,
    J. Théor. Nombres Bordeaux 9 (1), pp. 221–228.
    Show Annotations
    External Links:
    ISSN 1246-7405, PostScript, MathReview (L. Skula), ZentralBlatt.
    Referenced by:
    §24.16(iii).
    Encodings:
    BibTeX
  • E. Kanzieper (2002)
    Replica field theories, Painlevé transcendents, and exact correlation functions,
    Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).
    Show Annotations
    External Links:
    ISSN 0031-9007, Document, MathReview.
    Referenced by:
    ‣ §32.16.
    Encodings:
    BibTeX
  • A. A. Kapaev and A. V. Kitaev (1993)
    Connection formulae for the first Painlevé transcendent in the complex domain,
    Lett. Math. Phys. 27 (4), pp. 243–252.
    Show Annotations
    External Links:
    ISSN 0377-9017, Document, MathReview (B. L. J. Braaksma), ZentralBlatt.
    Referenced by:
    §32.11(i), §32.12(i).
    Encodings:
    BibTeX
  • A. A. Kapaev (1988)
    Asymptotic behavior of the solutions of the Painlevé equation of the first kind,
    Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: Differential Equations 24(1988), no. 10, pp. 1107–1115 (1989)
    External Links:
    ISSN 0374-0641, MathReview, ZentralBlatt.
    Referenced by:
    §32.11(i).
    Encodings:
    BibTeX
  • A. A. Kapaev (1991)
    Essential singularity of the Painlevé function of the second kind and the nonlinear Stokes phenomenon,
    Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 187, pp. 139–170 (Russian).
    Show Annotations
    Notes:
    English translation: J. Math. Sci. 73(1995), no. 4, pp. 500–517
    External Links:
    ISSN 0373-2703, Document, MathReview (Andreĭ Bolibrukh), ZentralBlatt.
    Referenced by:
    §32.12(ii).
    Encodings:
    BibTeX
  • A. A. Kapaev (2004)
    Quasi-linear Stokes phenomenon for the Painlevé first equation,
    J. Phys. A 37 (46), pp. 11149–11167.
    Show Annotations
    External Links:
    ISSN 0305-4470, Document, MathReview (W. Balser), ZentralBlatt.
    Referenced by:
    §32.12(i).
    Encodings:
    BibTeX
  • N. S. Kapany and J. J. Burke (1972)
    Optical Waveguides,
    Quantum Electronics - Principles and Applications, Academic Press, New York.
    Show Annotations
    External Links:
    ISBN 0-12-396760-0.
    Referenced by:
    §10.73(i).
    Encodings:
    BibTeX
  • P. L. Kapitsa (1951a)
    Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal,
    Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.
    Show Annotations
    External Links:
    MathReview (N. A. Hall).
    Referenced by:
    §10.73(v).
    Encodings:
    BibTeX
  • P. L. Kapitsa (1951b)
    The computation of the sums of negative even powers of roots of Bessel functions,
    Doklady Akad. Nauk SSSR (N.S.) 77, pp. 561–564.
    Show Annotations
    External Links:
    MathReview (A. Erdélyi).
    Referenced by:
    §10.21(xiii).
    Encodings:
    BibTeX
  • E. L. Kaplan (1948)
    Auxiliary table for the incomplete elliptic integrals,
    J. Math. Physics 27, pp. 11–36.
    Show Annotations
    External Links:
    MathReview (S. C. van Veen), ZentralBlatt.
    Referenced by:
    §19.12.
    Encodings:
    BibTeX
  • A. A. Karatsuba and S. M. Voronin (1992)
    The Riemann Zeta-Function,
    de Gruyter Expositions in Mathematics, Vol. 5, Walter de Gruyter & Co., Berlin.
    Show Annotations
    Notes:
    Translated from the Russian by Neal Koblitz
    External Links:
    ISBN 3-11-013170-6, MathReview (Matti Jutila), ZentralBlatt.
    Referenced by:
    Ch.25.
    Encodings:
    BibTeX
  • S. Karlin and J. L. McGregor (1961)
    The Hahn polynomials, formulas and an application,
    Scripta Math. 26, pp. 33–46.
    Show Annotations
    External Links:
    MathReview (L. J. Slater), ZentralBlatt.
    Referenced by:
    §18.20(i), §18.21(ii), §18.26(ii).
    Encodings:
    BibTeX
  • D. Karp, A. Savenkova and S. M. Sitnik (2007)
    Series expansions for the third incomplete elliptic integral via partial fraction decompositions,
    J. Comput. Appl. Math. 207 (2), pp. 331–337.
    Show Annotations
    External Links:
    ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt.
    Referenced by:
    §19.12, §19.5.
    Encodings:
    BibTeX
  • D. Karp and S. M. Sitnik (2007)
    Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity,
    J. Comput. Appl. Math. 205 (1), pp. 186–206.
    Show Annotations
    External Links:
    ISSN 0377-0427, Document, FullText, MathReview (José Luis López), ZentralBlatt.
    Referenced by:
    §19.12, §19.12, §19.36(iv), §19.36(iv).
    Encodings:
    BibTeX
  • K. A. Karpov and È. A. Čistova (1964)
    Tablitsy funktsii Vebera. Tom II,
    Vičisl. Centr Akad. Nauk SSSR, Moscow (Russian).
    Show Annotations
    External Links:
    MathReview (John Todd), ZentralBlatt.
    Referenced by:
    §12.19.
    Encodings:
    BibTeX
  • K. A. Karpov and È. A. Čistova (1968)
    Tablitsy funktsii Vebera. Tom III,
    Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
    Show Annotations
    External Links:
    MathReview (Walter Gautschi).
    Referenced by:
    §12.19.
    Encodings:
    BibTeX
  • A. V. Kashevarov (1998)
    The second Painlevé equation in electric probe theory. Some numerical solutions,
    Zh. Vychisl. Mat. Mat. Fiz. 38 (6), pp. 992–1000 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: Comput. Math. Math. Phys. 38(1998), no. 6, pp. 950–958
    External Links:
    ISSN 0044-4669, MathReview, ZentralBlatt.
    Referenced by:
    §32.17.
    Encodings:
    BibTeX
  • A. V. Kashevarov (2004)
    The second Painlevé equation in the electrostatic probe theory: Numerical solutions for the partial absorption of charged particles by the surface,
    Technical Physics 49 (1), pp. 1–7.
    Show Annotations
    External Links:
    Document.
    Referenced by:
    §32.17.
    Encodings:
    BibTeX
  • C. Kassel (1995)
    Quantum Groups,
    Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.
    Show Annotations
    External Links:
    ISBN 0-387-94370-6, MathReview (Yu. N. Bespalov), ZentralBlatt.
    Referenced by:
    §17.17.
    Encodings:
    BibTeX
  • N. M. Katz (1975)
    The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers,
    Math. Ann. 216 (1), pp. 1–4.
    Show Annotations
    External Links:
    ISSN 0025-5831, Document, MathReview (M. Basmakov), ZentralBlatt.
    Referenced by:
    §24.16(iii).
    Encodings:
    BibTeX
  • E. H. Kaufman and T. D. Lenker (1986)
    Linear convergence and the bisection algorithm,
    Amer. Math. Monthly 93 (1), pp. 48–51.
    Show Annotations
    External Links:
    ISSN 0002-9890, FullText, MathReview (J. G. Herriot), ZentralBlatt.
    Referenced by:
    ‣ §3.8(iii).
    Encodings:
    BibTeX
  • A. Ya. Kazakov and S. Yu. Slavyanov (1996)
    Integral equations for special functions of Heun class,
    Methods Appl. Anal. 3 (4), pp. 447–456.
    Show Annotations
    External Links:
    ISSN 1073-2772, FullText, MathReview, ZentralBlatt.
    Referenced by:
    ‣ §31.10(ii).
    Encodings:
    BibTeX
  • N. D. Kazarinoff (1988)
    Special functions and the Bieberbach conjecture,
    Amer. Math. Monthly 95 (8), pp. 689–696.
    Show Annotations
    External Links:
    ISSN 0002-9890, FullText, MathReview (S. L. Shukla), ZentralBlatt.
    Referenced by:
    §16.23(iii).
    Encodings:
    BibTeX
  • R. B. Kearfott, M. Dawande, K. Du and C. Hu (1994)
    Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library,
    ACM Trans. Math. Software 20 (4), pp. 447–459.
    Show Annotations
    External Links:
    ISSN 0098-3500, Document, TOMS module 737 (in GAMS), ZentralBlatt.
    Referenced by:
    §4.48(ii).
    Encodings:
    BibTeX
  • R. B. Kearfott (1996)
    Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type,
    ACM Trans. Math. Software 22 (4), pp. 385–392.
    Show Annotations
    External Links:
    ISSN 0098-3500, Document, TOMS module 763 (in GAMS), ZentralBlatt.
    Referenced by:
    §4.48(ii).
    Encodings:
    BibTeX
  • J. P. Keating (1999)
    Periodic Orbits, Spectral Statistics, and the Riemann Zeros,
    in Supersymmetry and Trace Formulae: Chaos and Disorder,
    (D. E. Khmelnitskii and I. V. Lerner Eds.), pp. 1–15.
    Show Annotations
    Referenced by:
    §25.17.
    Encodings:
    BibTeX
  • J. Keating (1993)
    The Riemann Zeta-Function and Quantum Chaology,
    in Quantum Chaos (Varenna, 1991),
    Proc. Internat. School of Phys. Enrico Fermi, CXIX, pp. 145–185.
    Show Annotations
    External Links:
    MathReview (Dieter H. Mayer).
    Referenced by:
    §25.17.
    Encodings:
    BibTeX
  • R. P. Kelisky (1957)
    On formulas involving both the Bernoulli and Fibonacci numbers,
    Scripta Math. 23, pp. 27–35.
    Show Annotations
    External Links:
    MathReview (L. Carlitz), ZentralBlatt.
    Referenced by:
    §24.15(iv).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1984a)
    Calculation of modified Bessel functions in a complex domain,
    Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 24(3), pp. 15–24
    External Links:
    ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt.
    Referenced by:
    §10.42, §10.74(iv).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1984b)
    Calculation of the complex zeros of the modified Bessel function of the second kind and its derivatives,
    Zh. Vychisl. Mat. i Mat. Fiz. 24 (8), pp. 1150–1163.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 24(4), pp. 115–123
    External Links:
    ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt.
    Referenced by:
    §10.42, ‣ §10.74(vi), §10.75(vi).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1984c)
    Evaluation of complex zeros of Bessel functions J_{\nu}(z) and I_{\nu}(z) and their derivatives,
    Zh. Vychisl. Mat. i Mat. Fiz. 24 (10), pp. 1497–1513.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 24(5), pp. 131–141
    External Links:
    ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt.
    Referenced by:
    §10.21(ix), ‣ §10.74(vi), §10.75(vi).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1985a)
    Calculation of the complex zeros of a Bessel function of the second kind and its derivatives,
    Zh. Vychisl. Mat. i Mat. Fiz. 25 (10), pp. 1457–1473, 1581 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: USSR Comput. Math. Math. Phys., 25(1985), no. 5, pp. 117–128.
    External Links:
    ISSN 0044-4669, Document, MathReview (Jiří Hřebíček), ZentralBlatt.
    Referenced by:
    §10.21(i), §10.21(ix), ‣ §10.74(vi), ‣ §10.75(iii).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1985b)
    Calculation of the complex zeros of Hankel functions and their derivatives,
    Zh. Vychisl. Mat. i Mat. Fiz. 25 (11), pp. 1628–1643, 1741.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 25(6), pp. 26–36
    External Links:
    ISSN 0044-4669, Document, MathReview (E. Riekstiņš), ZentralBlatt.
    Referenced by:
    §10.21(ix), ‣ §10.74(vi), ‣ §10.75(iii), §10.75(vi).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1985c)
    Calculation of the multiple zeros of the derivatives of the cylindrical Bessel functions J_{\nu}(z) and Y_{\nu}(z),
    Zh. Vychisl. Mat. i Mat. Fiz. 25 (12), pp. 1749–1760, 1918.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 25(6), pp. 101–107
    External Links:
    ISSN 0044-4669, Document, MathReview (E. Riekstiņš), ZentralBlatt.
    Referenced by:
    ‣ §10.74(vi), ‣ §10.75(iii).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1986)
    On multiple zeros of derivatives of Bessel’s cylindrical functions,
    Dokl. Akad. Nauk SSSR 288 (2), pp. 285–288 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: Soviet Math. Dokl. 33(3), 650–653, (1986).
    External Links:
    ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt.
    Referenced by:
    §10.21(i), ‣ §10.74(vi).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1987)
    On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions,
    Zh. Vychisl. Mat. i Mat. Fiz. 27 (11), pp. 1628–1639, 1758.
    Show Annotations
    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 27(6), pp. 18–25
    External Links:
    ISSN 0044-4669, Document, MathReview (Hans-Jürgen Albrand), ZentralBlatt.
    Referenced by:
    §10.21(ix), ‣ §10.74(vi), ‣ §10.75(iii).
    Encodings:
    BibTeX
  • M. K. Kerimov and S. L. Skorokhodov (1988)
    Multiple complex zeros of derivatives of the cylindrical Bessel functions,
    Dokl. Akad. Nauk SSSR 299 (3), pp. 614–618 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: Soviet Phys. Dokl. 33(3),196–198, (1988).
    External Links:
    ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt.
    Referenced by:
    §10.21(ix), ‣ §10.74(vi).
    Encodings:
    BibTeX
  • M. K. Kerimov (1980)
    Methods of computing the Riemann zeta-function and some generalizations of it,
    USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
    Show Annotations
    External Links:
    Document, MathReview (Matti Jutila), ZentralBlatt.
    Referenced by:
    §25.18(i).
    Encodings:
    BibTeX
  • M. K. Kerimov (1999)
    The Rayleigh function: Theory and computational methods,
    Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.
    Show Annotations
    Notes:
    Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.
    External Links:
    ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt.
    Referenced by:
    §10.21(xiii).
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  • M. K. Kerimov (2008)
    Overview of some new results concerning the theory and applications of the Rayleigh special function,
    Comput. Math. Math. Phys. 48 (9), pp. 1454–1507.
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    External Links:
    ISSN 0965-5425, Document, FullText.
    Referenced by:
    §10.21(xiii), §10.21(xiii).
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  • M. Kerker (1969)
    The Scattering of Light and Other Electromagnetic Radiation,
    Academic Press, New York.
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    External Links:
    ISBN 0-12-404550-2.
    Referenced by:
    §10.73(i).
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  • A. D. Kerr (1978)
    An indirect method for evaluating certain infinite integrals,
    Z. Angew. Math. Phys. 29 (3), pp. 380–386.
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    External Links:
    ISSN 0044-2275, Document, MathReview, ZentralBlatt.
    Referenced by:
    §10.71(ii).
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  • R. P. Kerr (1963)
    Gravitational field of a spinning mass as an example of algebraically special metrics,
    Phys. Rev. Lett. 11 (5), pp. 237–238.
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    External Links:
    Document, MathReview (C. Gilbert), ZentralBlatt.
    Referenced by:
    §31.17(ii).
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  • D. Kershaw (1983)
    Some extensions of W. Gautschi’s inequalities for the gamma function,
    Math. Comp. 41 (164), pp. 607–611.
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    External Links:
    ISSN 0025-5718, FullText, MathReview (P. Anandani), ZentralBlatt.
    Referenced by:
    §5.6(i).
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  • S. Kesavan and A. S. Vasudevamurthy (1985)
    On some boundary element methods for the heat equation,
    Numer. Math. 46 (1), pp. 101–120.
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    External Links:
    ISSN 0029-599X, Document, MathReview (Reinhard Scholz), ZentralBlatt.
    Referenced by:
    §7.8.
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  • S. H. Khamis (1965)
    Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution,
    Justus von Liebig Verlag, Darmstadt (German, English).
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    Notes:
    In cooperation with W. Rudert
    External Links:
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    Referenced by:
    §8.26(ii).
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  • A. Khare, A. Lakshminarayan and U. Sukhatme (2003)
    Cyclic identities for Jacobi elliptic and related functions,
    J. Math. Phys. 44 (4), pp. 1822–1841.
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    External Links:
    ISSN 0022-2488, Document, MathReview (Zhi Guo Liu), ZentralBlatt.
    Referenced by:
    §22.9(iv), §22.9(v).
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  • A. Khare and U. Sukhatme (2002)
    Cyclic identities involving Jacobi elliptic functions,
    J. Math. Phys. 43 (7), pp. 3798–3806.
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    External Links:
    ISSN 0022-2488, Document, MathReview, ZentralBlatt.
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  • A. Khare and U. Sukhatme (2004)
    Connecting Jacobi elliptic functions with different modulus parameters,
    Pramana 63 (5), pp. 921–936.
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    External Links:
    Pdf, Document.
    Referenced by:
    §22.7(iii).
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  • A. I. Kheyfits (2004)
    Closed-form representations of the Lambert W function,
    Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
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    External Links:
    ISSN 1311-0454, MathReview (Lewis H. Ryder), ZentralBlatt.
    Referenced by:
    §4.13.
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  • H. Ki and Y. Kim (2000)
    On the zeros of some generalized hypergeometric functions,
    J. Math. Anal. Appl. 243 (2), pp. 249–260.
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    External Links:
    ISSN 0022-247X, Document, MathReview (M. K. Jain), ZentralBlatt.
    Referenced by:
    §16.9.
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  • S. Kida (1981)
    A vortex filament moving without change of form,
    J. Fluid Mech. 112, pp. 397–409.
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    External Links:
    ISSN 0022-1120, Document, MathReview, ZentralBlatt.
    Referenced by:
    §19.35(ii).
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  • S. K. Kim (1972)
    The asymptotic expansion of a hypergeometric function \mathop{{{}_{{2}}F_{{2}}}\/}\nolimits\!\left(1,\alpha;\rho _{1},\rho _{2};z\right),
    Math. Comp. 26 (120), pp. 963.
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    External Links:
    FullText, MathReview, ZentralBlatt.
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    ‣ §16.11(ii).
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  • T. Kim and H. S. Kim (1999)
    Remark on p-adic q-Bernoulli numbers,
    Adv. Stud. Contemp. Math. (Pusan) 1, pp. 127–136.
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    Notes:
    Algebraic number theory (Hapcheon/Saga, 1996)
    External Links:
    ISSN 1229-3067, MathReview (L. Skula), ZentralBlatt.
    Referenced by:
    §24.16(iii).
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  • N. Kimura (1988)
    On the degree of an irreducible factor of the Bernoulli polynomials,
    Acta Arith. 50 (3), pp. 243–249.
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    External Links:
    ISSN 0065-1036, Pdf, MathReview (Wells Johnson), ZentralBlatt.
    Referenced by:
    §24.12(iii).
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  • B. J. King, R. V. Baier and S. Hanish (1970)
    A Fortran computer program for calculating the prolate spheroidal radial functions of the first and second kind and their first derivatives,
    NRL Report No. 7012
    Naval Res. Lab.  Washingtion, D. C..
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    Referenced by:
    §30.18(iii).
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  • B. J. King and A. L. Van Buren (1973)
    A general addition theorem for spheroidal wave functions,
    SIAM J. Math. Anal. 4 (1), pp. 149–160.
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    External Links:
    Document, MathReview (J. Meixner), ZentralBlatt.
    Referenced by:
    §30.10.
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  • B. J. King and A. L. Van Buren (1970)
    A Fortran computer program for calculating the prolate and oblate angle functions of the first kind and their first and second derivatives,
    NRL Report No. 7161
    Naval Res. Lab.  Washingtion, D. C..
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    Referenced by:
    §30.18(iii).
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  • I. Ye. Kireyeva and K. A. Karpov (1961)
    Tables of Weber functions. Vol. I,
    Mathematical Tables Series, Vol. 15, Pergamon Press, London-New York.
    Show Annotations
    Notes:
    Translated by Prasenjit Basu
    External Links:
    MathReview (F. W. J. Olver), ZentralBlatt.
    Referenced by:
    §12.19.
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  • A. N. Kirillov (1995)
    Dilogarithm identities,
    Progr. Theoret. Phys. Suppl. (118), pp. 61–142.
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    External Links:
    ISSN 0375-9687, FullText, MathReview (J. Browkin), ZentralBlatt.
    Referenced by:
    §25.12(i).
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  • N. P. Kirk, J. N. L. Connor and C. A. Hobbs (2000)
    An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives,
    Computer Physics Comm. 132 (1-2), pp. 142–165.
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    External Links:
    Document, Code, ZentralBlatt.
    Referenced by:
    §36.15(iii).
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  • E. T. Kirkpatrick (1960)
    Tables of values of the modified Mathieu functions,
    Math. Comp. 14, pp. 118–129.
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    External Links:
    FullText, MathReview (L. J. Slater), ZentralBlatt.
    Referenced by:
    §28.35(i).
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  • A. V. Kitaev, C. K. Law and J. B. McLeod (1994)
    Rational solutions of the fifth Painlevé equation,
    Differential Integral Equations 7 (3-4), pp. 967–1000.
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    External Links:
    ISSN 0893-4983, MathReview, ZentralBlatt.
    Referenced by:
    §32.8(v).
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  • A. V. Kitaev and A. H. Vartanian (2004)
    Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I,
    Inverse Problems 20 (4), pp. 1165–1206.
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    External Links:
    ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt.
    Referenced by:
    §32.11(iv).
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  • A. V. Kitaev (1987)
    The method of isomonodromic deformations and the asymptotics of the solutions of the “complete” third Painlevé equation,
    Mat. Sb. (N.S.) 134(176) (3), pp. 421–444, 448 (Russian).
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    Notes:
    In Russian. English translation: Math. USSR-Sb. 62(1989), no. 2, pp. 421–444.
    External Links:
    ISSN 0368-8666, RussianText, Document, MathReview (J. Chrastina), ZentralBlatt.
    Referenced by:
    §32.11(iv).
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  • A. V. Kitaev (1994)
    Elliptic asymptotics of the first and second Painlevé transcendents,
    Uspekhi Mat. Nauk 49 (1(295)), pp. 77–140 (Russian).
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    Notes:
    In Russian. English translation: Russian Math. Surveys 49(1994), no. 1, pp. 81–150.
    External Links:
    ISSN 0042-1316, Document, MathReview (V. A. Golubeva), ZentralBlatt.
    Referenced by:
    §32.11(i), §32.12(ii).
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  • Y. Kivshar and B. Luther-Davies (1998)
    Dark optical solitons: Physics and applications,
    Physics Reports 298 (2-3), pp. 81–197.
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    External Links:
    Document.
    Referenced by:
    §22.19(iii).
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  • F. Klein (1894)
    Vorlesungen über die hypergeometrische Funktion,
    Göttingen (German).
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    Notes:
    Reprint by Springer-Verlag, Berlin, 1981, of the 1933 original.
    External Links:
    ISBN 3-540-10455-0, MathReview (J. S. Joel), ZentralBlatt.
    Referenced by:
    §15.17(ii).
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  • A. Kneser (1927)
    Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen,
    Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).
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    External Links:
    ZentralBlatt.
    Referenced by:
    §19.5.
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  • H. Kneser (1950)
    Reelle analytische Lösungen der Gleichung \varphi(\varphi(x))=e^{x} und verwandter Funktionalgleichungen,
    J. Reine Angew. Math. 187, pp. 56–67.
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    External Links:
    ISSN 0075-4102, MathReview (G. Valiron), ZentralBlatt.
    Referenced by:
    §4.12.
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  • K. Knopp (1948)
    Theory and Application of Infinite Series,
    2nd edition, Hafner, New York.
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    Notes:
    R. C. Young, translator.
    Referenced by:
    §25.2(iii).
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  • K. Knopp (1964)
    Theorie und Anwendung der unendlichen Reihen,
    4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).
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    Notes:
    A translation by R. C. Young appeared in 1928, Theory and Application of Infinite Series, Blackie, 571pp.
    External Links:
    MathReview, ZentralBlatt.
    Referenced by:
    §3.9(ii).
    Encodings:
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  • U. J. Knottnerus (1960)
    Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters,
    J. B. Wolters, Groningen.
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    External Links:
    MathReview (L. J. Slater), ZentralBlatt.
    Referenced by:
    §16.11(iii).
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  • D. E. Knuth and T. J. Buckholtz (1967)
    Computation of tangent, Euler, and Bernoulli numbers,
    Math. Comp. 21 (100), pp. 663–688.
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    External Links:
    FullText, MathReview, ZentralBlatt.
    Referenced by:
    §24.15(ii), §24.19(i).
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  • D. E. Knuth (1968)
    The Art of Computer Programming. Vol. 1: Fundamental Algorithms,
    1st edition, Addison-Wesley Publishing Co., Reading, MA-London-Don Mills, Ont.
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    Notes:
    Second printing of second edition by Addison-Wesley Publishing Co., Reading, MA-London-Amsterdam, 1975.
    External Links:
    MathReview (M. Muller), ZentralBlatt.
    Referenced by:
    §1.4(iii).
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  • D. E. Knuth (1986)
    METAFONT: The Program,
    Computers and Typesetting, Vol. D, Addison-Wesley, Reading, MA.
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    External Links:
    ISBN 0-201-13438-1, ZentralBlatt.
    Referenced by:
    §3.11(vi).
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  • D. E. Knuth (1992)
    Two notes on notation,
    Amer. Math. Monthly 99 (5), pp. 403–422.
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    External Links:
    ISSN 0002-9890, FullText, MathReview (W. Dörfler), ZentralBlatt.
    Referenced by:
    ‣ §26.1, ‣ §26.1.
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  • D. E. Knuth (1993)
    The Stanford GraphBase,
    ACM Press, New York.
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    External Links:
    ISBN 0201542757, ZentralBlatt.
    Referenced by:
    §26.22.
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  • N. Koblitz (1984)
    p-adic Numbers, p-adic Analysis, and Zeta-Functions,
    2nd edition, Graduate Texts in Mathematics, Vol. 58, Springer-Verlag, New York.
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    External Links:
    ISBN 0-387-96017-1, MathReview, ZentralBlatt.
    Referenced by:
    §24.17(iii).
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  • N. Koblitz (1993)
    Introduction to Elliptic Curves and Modular Forms,
    2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.
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    External Links:
    ISBN 0-387-97966-2, MathReview, ZentralBlatt.
    Referenced by:
    §20.10(i), §20.12(i), §20.9(iii), §22.18(iv), ‣ §23.1, §23.20(ii), §23.20(v), Ch.23.
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  • N. Koblitz (1999)
    Algebraic Aspects of Cryptography,
    Springer-Verlag, Berlin.
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    Notes:
    Second printing with corrections
    External Links:
    ISBN 3-540-63446-0, MathReview (M. V. D. Burmester), ZentralBlatt.
    Referenced by:
    §23.20(iii).
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  • M. Kodama (2008)
    Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument,
    ACM Trans. Math. Software 34 (4), pp. Art. 22, 21.
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    External Links:
    ISSN 0098-3500, Document, MathReview Entry.
    Referenced by:
    §10.77(vii).
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  • M. Koecher (1954)
    Zur Theorie der Modulformen n-ten Grades. I,
    Math. Z. 59, pp. 399–416 (German).
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    External Links:
    ISSN 0025-5874, Document, MathReview (H. S. Zuckerman), ZentralBlatt.
    Referenced by:
    §35.6(i).
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  • J. Koekoek, R. Koekoek and H. Bavinck (1998)
    On differential equations for Sobolev-type Laguerre polynomials,
    Trans. Amer. Math. Soc. 350 (1), pp. 347–393.
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    External Links:
    ISSN 0002-9947, FullText, MathReview (Hans W. Volkmer), ZentralBlatt.
    Referenced by:
    §18.36(ii).
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  • R. Koekoek, P. A. Lesky and R. F. Swarttouw (2010)
    Hypergeometric Orthogonal Polynomials and Their q-Analogues,
    Springer Monographs in Mathematics, Springer-Verlag, Berlin.
    Show Annotations
    Notes:
    With a foreword by Tom H. Koornwinder
    External Links:
    ISBN 978-3-642-05013-8, Document, FullText, MathReview (Jeremy Lovejoy), ZentralBlatt.
    Referenced by:
    §18.1(iii), §18.22(ii), §18.26(iii), §18.27(i), §18.27(ii), §18.27(iii), §18.27(iv), §18.27(v), §18.28(i), §18.28(ii), §18.28(iii), §18.28(viii), Ch.18, Roelof Koekoek.
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  • W. Koepf (1999)
    Orthogonal polynomials and computer algebra,
    (J. Kajiwara and Y. S. Xu Eds.), Int. Soc. Anal. Appl. Comput., Vol. 4, Dordrecht, pp. 205–234.
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    External Links:
    FullText, MathReview Entry, ZentralBlatt.
    Referenced by:
    CAOP (Web Site).
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  • P. Koev and A. Edelman (2006)
    The efficient evaluation of the hypergeometric function of a matrix argument,
    Math. Comp. 75 (254), pp. 833–846.
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    Notes:
    For Matlab software for this function, see Plamen Koev’s home page.
    External Links:
    Home Page, ISSN 0025-5718, Document, MathReview (Luis Verde-Star), ZentralBlatt.
    Referenced by:
    §35.10, §35.12.
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  • D. A. Kofke (2004)
    Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)],
    J. Chem. Phys. 121 (2), pp. 1167.
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    External Links:
    Document.
    Referenced by:
    §8.24(ii).
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  • S. Koizumi (1976)
    Theta relations and projective normality of Abelian varieties,
    Amer. J. Math. 98 (4), pp. 865–889.
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    External Links:
    FullText, MathReview (T. Oda), ZentralBlatt.
    Referenced by:
    §21.6(ii).
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  • G. C. Kokkorakis and J. A. Roumeliotis (1998)
    Electromagnetic eigenfrequencies in a spheroidal cavity (calculation by spheroidal eigenvectors),
    J. Electromagn. Waves Appl. 12 (12), pp. 1601–1624.
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    External Links:
    ISSN 0920-5071, Document, MathReview, ZentralBlatt.
    Referenced by:
    §30.14(v).
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  • C. G. Kokologiannaki, P. D. Siafarikas and C. B. Kouris (1992)
    On the complex zeros of H_{{\mu}}(z),\ {\mathop{J_{{\mu}}\/}\nolimits^{{\prime}}}\!\left(z\right),\ {\mathop{J_{{\mu}}\/}\nolimits^{{\prime\prime}}}\!\left(z\right) for real or complex order,
    J. Comput. Appl. Math. 40 (3), pp. 337–344.
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    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt.
    Referenced by:
    §10.21(ix).
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  • G. A. Kolesnik (1969)
    An improvement of the remainder term in the divisor problem,
    Mat. Zametki 6, pp. 545–554 (Russian).
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    Notes:
    In Russian. English translation: Math. Notes 6(1969), no. 5, pp. 784–791.
    External Links:
    Document, MathReview (A. I. Vinogradov), ZentralBlatt.
    Referenced by:
    §27.11.
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  • I. V. Komarov, L. I. Ponomarev and S. Yu. Slavyanov (1976)
    Sferoidalnye i kulonovskie sferoidalnye funktsii,
    Izdat. “Nauka”, Moscow (Russian).
    Show Annotations
    Notes:
    Translated title: Spheroidal and Coulomb Spheroidal Functions
    External Links:
    MathReview.
    Referenced by:
    §30.12, Ch.30, §31.13.
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  • E. Konishi (1996)
    Calculation of complex polygamma functions,
    Sci. Rep. Hirosaki Univ. 43 (1), pp. 161–183.
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    External Links:
    ISSN 0367-6439, MathReview, ZentralBlatt.
    Referenced by:
    §5.24(iv).
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  • E. J. Konopinski (1981)
    Electromagnetic Fields and Relativistic Particles,
    International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.
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    External Links:
    ISBN 0-07-035264-X, MathReview (George Zipfel, Jr.).
    Referenced by:
    ‣ §1.17(ii), §10.73(ii).
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  • T. H. Koornwinder and I. Sprinkhuizen-Kuyper (1978)
    Hypergeometric functions of 2\times 2 matrix argument are expressible in terms of Appel’s functions F_{{4}},
    Proc. Amer. Math. Soc. 70 (1), pp. 39–42.
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    External Links:
    FullText, MathReview (P. N. Rathie), ZentralBlatt.
    Referenced by:
    §35.7(ii).
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  • T. H. Koornwinder (1974)
    Jacobi polynomials. II. An analytic proof of the product formula,
    SIAM J. Math. Anal. 5, pp. 125–137.
  • T. H. Koornwinder (1975a)
    A new proof of a Paley-Wiener type theorem for the Jacobi transform,
    Ark. Mat. 13, pp. 145–159.
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    External Links:
    Document, MathReview (G. Gasper), ZentralBlatt.
    Referenced by:
    ‣ §18.10(i).
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  • T. H. Koornwinder (1975b)
    Jacobi polynomials. III. An analytic proof of the addition formula,
    SIAM. J. Math. Anal. 6, pp. 533–543.
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    External Links:
    Document, MathReview (G. Gasper), ZentralBlatt.
    Referenced by:
    ‣ §18.18(ii).
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  • T. H. Koornwinder (1975c)
    Two-variable Analogues of the Classical Orthogonal Polynomials,
    in Theory and Application of Special Functions,
    pp. 435–495.
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    External Links:
    MathReview (R. A. Askey), ZentralBlatt.
    Referenced by:
    §18.37(ii).
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  • T. H. Koornwinder (1977)
    The addition formula for Laguerre polynomials,
    SIAM J. Math. Anal. 8 (3), pp. 535–540.
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    External Links:
    Document, MathReview (M. Mikolas), ZentralBlatt.
    Referenced by:
    §18.14(i), ‣ §18.17(ii).
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  • T. H. Koornwinder (1984a)
    Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups,
    in Special Functions: Group Theoretical Aspects and Applications,
    pp. 1–85.
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    Notes:
    Reprinted by Kluwer Academic Publishers, Boston, 2002.
    External Links:
    ISBN 90-277-1822-9; 1-4020-0319-6, MathReview (Jacques Faraut), ZentralBlatt.
    Referenced by:
    §14.31(ii), §15.17(iii), §15.9(ii).
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  • T. H. Koornwinder (1984b)
    Orthogonal polynomials with weight function (1-x)^{{\alpha}}(1+x)^{{\beta}}+M\delta(x+1)+N\delta(x-1),
    Canad. Math. Bull. 27 (2), pp. 205–214.
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    External Links:
    ISSN 0008-4395, MathReview (Wolfgang Hahn), ZentralBlatt.
    Referenced by:
    §18.36(i), §18.36(i).
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  • T. H. Koornwinder (1989)
    Meixner-Pollaczek polynomials and the Heisenberg algebra,
    J. Math. Phys. 30 (4), pp. 767–769.
    Show Annotations
    External Links:
    ISSN 0022-2488, Document, MathReview, ZentralBlatt.
    Referenced by:
    §18.21(ii).
    Encodings:
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  • T. H. Koornwinder (1992)
    Askey-Wilson Polynomials for Root Systems of Type BC,
    in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991),
    Contemp. Math., Vol. 138, pp. 189–204.
    Show Annotations
    External Links:
    FullText, MathReview (Eric M. Opdam), ZentralBlatt.
    Referenced by:
    §18.37(iii).
    Encodings:
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  • T. H. Koornwinder (2006)
    Lowering and Raising Operators for Some Special Orthogonal Polynomials,
    in Jack, Hall-Littlewood and Macdonald Polynomials,
    Contemp. Math., Vol. 417, pp. 227–238.
    Show Annotations
    External Links:
    FullText, MathReview Entry, ZentralBlatt.
    Referenced by:
    §18.9(iii).
    Encodings:
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  • T. H. Koornwinder (2009)
    The Askey scheme as a four-manifold with corners,
    Ramanujan J. 20 (3), pp. 409–439.
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    External Links:
    ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt.
    Referenced by:
    §18.26(v), §18.26(v).
    Encodings:
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  • Koornwinder (Web Site)
    Tom Koornwinder’s Personal Collection of Maple Procedures.
    Show Annotations
    External Links:
    Home Page.
    Referenced by:
    § ‣ § Software Cross Index.
    Encodings:
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  • B. G. Korenev (2002)
    Bessel Functions and their Applications,
    Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
    Show Annotations
    Notes:
    Translated from the Russian by E. V. Pankratiev
    External Links:
    ISBN 0-415-28130-X, MathReview (L. Debnath), ZentralBlatt.
    Referenced by:
    §10.73(i), §10.73(i), §10.73(i).
    Encodings:
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  • V. E. Korepin, N. M. Bogoliubov and A. G. Izergin (1993)
    Quantum Inverse Scattering Method and Correlation Functions,
    Cambridge University Press, Cambridge.
    Show Annotations
    External Links:
    ISBN 0-521-37320-4; 0-521-58646-1, MathReview (Makoto Idzumi), ZentralBlatt.
    Referenced by:
    §26.20.
    Encodings:
    BibTeX
  • N. M. Korobov (1958)
    Estimates of trigonometric sums and their applications,
    Uspehi Mat. Nauk 13 (4 (82)), pp. 185–192 (Russian).
    Show Annotations
    External Links:
    MathReview (R. A. Rankin), ZentralBlatt.
    Referenced by:
    ‣ §27.12.
    Encodings:
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  • S. Koumandos and M. Lamprecht (2010)
    Some completely monotonic functions of positive order,
    Math. Comp. 79 (271), pp. 1697–1707.
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    External Links:
    ISSN 0025-5718, Document, FullText, MathReview (Necdet Batir), ZentralBlatt.
    Referenced by:
    ‣ §5.6(i), §5.6(i).
    Encodings:
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  • V. Kourganoff (1952)
    Basic Methods in Transfer Problems. Radiative Equilibrium and Neutron Diffusion,
    Oxford University Press, Oxford.
    Show Annotations
    Notes:
    With the collaboration of I. W. Busbridge
    External Links:
    MathReview (S. Chandrasekhar), ZentralBlatt.
    Referenced by:
    §8.19(x), §8.24(iii).
    Encodings:
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  • J. J. Kovacic (1986)
    An algorithm for solving second order linear homogeneous differential equations,
    J. Symbolic Comput. 2 (1), pp. 3–43.
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    External Links:
    ISSN 0747-7171, MathReview, ZentralBlatt.
    Referenced by:
    §31.14(ii).
    Encodings:
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  • S. Kowalevski (1889)
    Sur le problème de la rotation d’un corps solide autour d’un point fixe,
    Acta Math. 12 (1), pp. 177–232 (French).
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    External Links:
    ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt.
    Referenced by:
    §22.19(iv).
    Encodings:
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  • C. Krattenthaler (1993)
    HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively q-binomial sums and basic hypergeometric series,
    Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
    Show Annotations
    Notes:
    Also published in J. Symbolic Comput. (1995), v. 20, no. 5–6, pp. 737–744.
    External Links:
    Code, Document, MathReview (G. Gasper), ZentralBlatt.
    Referenced by:
    §17.19.
    Encodings:
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  • P. Kravanja, O. Ragos, M. N. Vrahatis and F. A. Zafiropoulos (1998)
    ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument,
    Comput. Phys. Comm. 113 (2-3), pp. 220–238.
    Show Annotations
    Notes:
    Double-precision Fortran, maximum accuracy 25S.
    External Links:
    ISSN 0010-4655, Document, Code, ZentralBlatt.
    Referenced by:
    §10.77(x).
    Encodings:
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  • Y. A. Kravtsov (1964)
    Asymptotic solution of Maxwell’s equations near caustics,
    Izv. Vuz. Radiofiz. 7, pp. 1049–1056.
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    Referenced by:
    §36.14(i).
    Encodings:
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  • Y. A. Kravtsov (1968)
    Two new asymptotic methods in the theory of wave propagation in inhomogeneous media,
    Sov. Phys. Acoust. 14, pp. 1–17.
    Show Annotations
    External Links:
    ISSN 0038-562X.
    Referenced by:
    §36.14(iv).
    Encodings:
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  • Y. A. Kravtsov (1988)
    Rays and caustics as physical objects,
    in Progress in Optics,
    Vol. 26, pp. 227–348.
    Show Annotations
    External Links:
    ISBN 0444870962.
    Referenced by:
    §36.14(i).
    Encodings:
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  • R. Kress and E. Martensen (1970)
    Anwendung der Rechteckregel auf die reelle Hilberttransformation mit unendlichem Intervall,
    Z. Angew. Math. Mech. 50 (1-4), pp. T61–T64 (German).
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    External Links:
    MathReview (J. G. Herriot), ZentralBlatt.
    Referenced by:
    ‣ §3.5(ix).
    Encodings:
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  • E. Kreyszig (1957)
    On the zeros of the Fresnel integrals,
    Canad. J. Math. 9, pp. 118–131.
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    External Links:
    MathReview (W. C. Rheinboldt), ZentralBlatt.
    Referenced by:
    §7.13(iii).
    Encodings:
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  • I. M. Krichever (1976)
    An algebraic-geometrical construction of the Zakharov-Shabat equations and their periodic solutions,
    Sov. Math. Doklady 17, pp. 394–397.
    Show Annotations
    External Links:
    ZentralBlatt.
    Referenced by:
    Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2.
    Encodings:
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  • I. M. Krichever and S. P. Novikov (1989)
    Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces,
    Funktsional. Anal. i Prilozhen. 23 (1), pp. 24–40 (Russian).
    Show Annotations
    Notes:
    In Russian. English translation: Funct. Anal. Appl. 23(1989), no. 1, pp. 19–33
    External Links:
    ISSN 0374-1990, Document, MathReview (Fedor Malikov), ZentralBlatt.
    Referenced by:
    §20.12(ii).
    Encodings:
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  • T. Kriecherbauer and K. T.-R. McLaughlin (1999)
    Strong asymptotics of polynomials orthogonal with respect to Freud weights,
    Internat. Math. Res. Notices (6), pp. 299–333.
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    External Links:
    ISSN 1073-7928, Document, MathReview (Heinrich Begehr), ZentralBlatt.
    Referenced by:
    §18.32.
    Encodings:
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  • S. G. Krivoshlykov (1994)
    Quantum-Theoretical Formalism for Inhomogeneous Graded-Index Waveguides,
    Akademie Verlag, Berlin-New York.
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    External Links:
    ISBN 3-05-501598-3, MathReview (Apostolos Vourdas), ZentralBlatt.
    Referenced by:
    §10.73(i).
    Encodings:
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  • E. D. Krupnikov and K. S. Kölbig (1997)
    Some special cases of the generalized hypergeometric function \mathop{{{}_{{q+1}}F_{{q}}}\/}\nolimits,
    J. Comput. Appl. Math. 78 (1), pp. 79–95.
    Show Annotations
    External Links:
    ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt.
    Referenced by:
    §16.7.
    Encodings:
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  • M. D. Kruskal and P. A. Clarkson (1992)
    The Painlevé-Kowalevski and poly-Painlevé tests for integrability,
    Stud. Appl. Math. 86 (2), pp. 87–165.
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    External Links:
    ISSN 0022-2526, MathReview (Walter Strampp), ZentralBlatt.
    Referenced by:
    §32.2(i).
    Encodings:
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  • M. D. Kruskal (1974)
    The Korteweg-de Vries Equation and Related Evolution Equations,
    in Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972),
    Lectures in Appl. Math., Vol. 15, pp. 61–83.
    Show Annotations
    External Links:
    MathReview (G. L. Lamb, Jr.), ZentralBlatt.
    Referenced by:
    §22.19(iii).
    Encodings:
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  • V. I. Krylov and N. S. Skoblya (1985)
    A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation,
    Mir, Moscow.
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    Notes:
    Translated from the Russian by George Yankovsky. Reprint of the 1977 translation
    External Links:
    MathReview, ZentralBlatt.
    Referenced by:
    §3.5(viii).
    Encodings:
    BibTeX
  • H. Kuki (1972)
    Algorithm 421. Complex gamma function with error control,
    Comm. ACM 15 (4), pp. 271–272.
    Show Annotations
    External Links:
    ISSN 0001-0782, Document.
    Referenced by:
    §5.24(iv).
    Encodings:
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  • M. Kurz (1979)
    Fehlerabschätzungen zu asymptotischen Entwicklungen der Eigenwerte und Eigenlösungen der Mathieuschen Differentialgleichung,
    Ph.D. Thesis, Universität Duisburg-Essen, Essen, D 45177.
    Show Annotations
    Referenced by:
    §28.8(i).
    Encodings:
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  • V. B. Kuznetsov and S. Sahi (Eds.) (2006)
    Jack, Hall-Littlewood and Macdonald Polynomials,
    Contemporary Mathematics, Vol. 417, American Mathematical Society, Providence, RI.
    Show Annotations
    Notes:
    Proceedings of the workshop held in Edinburgh, September 23–26, 2003
    External Links:
    ISBN 0-8218-3683-8, MathReview Entry, ZentralBlatt.
    Referenced by:
    §18.37(iii).
    Encodings:
    BibTeX
  • V. B. Kuznetsov (1992)
    Equivalence of two graphical calculi,
    J. Phys. A 25 (22), pp. 6005–6026.
    Show Annotations
    External Links:
    ISSN 0305-4470, Document, MathReview (Niky Kamran), ZentralBlatt.
    Referenced by:
    §31.17(i).
    Encodings:
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  • K. H. Kwon, L. L. Littlejohn and G. J. Yoon (2006)
    Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions,
    J. Math. Anal. Appl. 324 (1), pp. 285–303.
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    External Links:
    ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt.
    Referenced by:
    §18.36(i).
    Encodings:
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  • K. S. Kölbig, J. A. Mignaco and E. Remiddi (1970)
    On Nielsen’s generalized polylogarithms and their numerical calculation,
    Nordisk Tidskr. Informationsbehandling (BIT) 10, pp. 38–73.
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    External Links:
    Document, MathReview (M. Nassif), ZentralBlatt.
    Referenced by:
    §25.12(i).
    Encodings:
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  • K. S. Kölbig (1968)
    Algorithm 327: Dilogarithm [S22],
    Comm. ACM 11 (4), pp. 270–271.
    Show Annotations
    Notes:
    Includes Algol program, maximum accuracy 12D.
    External Links:
    ISSN 0001-0782, Document.
    Referenced by:
    §25.21(v).
    Encodings:
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  • K. S. Kölbig (1970)
    Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function,
    Math. Comp. 24 (111), pp. 679–696.
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    External Links:
    FullText, MathReview, ZentralBlatt.
    Referenced by:
    §8.13(iii), §8.22(ii).
    Encodings:
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  • K. S. Kölbig (1972a)
    Complex zeros of two incomplete Riemann zeta functions,
    Math. Comp. 26 (118), pp. 551–565.
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    External Links:
    FullText, MathReview, ZentralBlatt.
    Referenced by:
    §8.22(ii).
    Encodings:
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  • K. S. Kölbig (1972b)
    On the zeros of the incomplete gamma function,
    Math. Comp. 26 (119), pp. 751–755.
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    External Links:
    FullText, MathReview, ZentralBlatt.
    Referenced by:
    §8.13(i), §8.13(iii), §8.13(iii).
    Encodings:
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  • K. S. Kölbig (1972c)
    Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument,
    Comput. Phys. Comm. 4, pp. 221–226.
    Show Annotations
    Notes:
    Single-precision Fortran, accuracy 12-14S
    External Links:
    Document, Code.
    Referenced by:
    §5.24(iv).
    Encodings:
    BibTeX
  • K. S. Kölbig (1981)
    A program for computing the conical functions of the first kind \mathop{P^{{m}}_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right) for m=0 and m=1,
    Comput. Phys. Comm. 23 (1), pp. 51–61.
    Show Annotations
    Notes:
    Single-precision Fortran, maximum accuracy 15D.
    External Links:
    Document, Code.
    Referenced by:
    §14.31(ii), §14.34(iv).
    Encodings:
    BibTeX
  • K. S. Kölbig (1986)
    Nielsen’s generalized polylogarithms,
    SIAM J. Math. Anal. 17 (5), pp. 1232–1258.
    Show Annotations
    External Links:
    ISSN 0036-1410, Document, MathReview (W. A. Al-Salam), ZentralBlatt.
    Referenced by:
    ‣ §25.12(ii).
    Encodings:
    BibTeX
  • T. W. Körner (1989)
    Fourier Analysis,
    2nd edition, Cambridge University Press, Cambridge.
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    External Links:
    ISBN 0-521-38991-7, MathReview, ZentralBlatt.
    Referenced by:
    §1.15(iii), §20.13.
    Encodings:
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