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  • V. Kac and P. Cheung (2002) Quantum Calculus, Universitext, Springer-Verlag, New York.
  • 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.
  • K. W. J. Kadell (1994) A proof of the q-Macdonald-Morris conjecture for BCn, Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
  • T. A. Kaeding (1995) Pascal program for generating tables of SU(3) Clebsch-Gordan coefficients, Comput. Phys. Comm. 85 (1), pp. 82–88.
  • 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.
  • D. K. Kahaner, C. Moler and S. Nash (1989) Numerical Methods and Software, Prentice Hall, Englewood Cliffs, NJ.
  • K. Kajiwara and T. Masuda (1999) On the Umemura polynomials for the Painlevé III equation, Phys. Lett. A 260 (6), pp. 462–467.
  • 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.
  • 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.
  • S. L. Kalla (1992) On the evaluation of the Gauss hypergeometric function, C. R. Acad. Bulgare Sci. 45 (6), pp. 35–36.
  • 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.
  • E. G. Kalnins, W. Miller and P. Winternitz (1976) The group O(4), separation of variables and the hydrogen atom, SIAM J. Appl. Math. 30 (4), pp. 630–664.
  • E. G. Kalnins and W. Miller (1991a) Hypergeometric expansions of Heun polynomials, SIAM J. Math. Anal. 22 (5), pp. 1450–1459.
  • E. G. Kalnins and W. Miller (1991b) Addendum: “Hypergeometric expansions of Heun polynomials”, SIAM J. Math. Anal. 22 (6), pp. 1803.
  • 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.
  • E. G. Kalnins (1986) Separation of Variables for Riemannian Spaces of Constant Curvature, Longman Scientific & Technical, Harlow.
  • A. Kalähne (1907) Über die Wurzeln einiger Zylinderfunktionen und gewisser aus ihnen gebildeter Gleichungen, Zeitschrift für Mathematik und Physik 54, pp. 55–86 (German).
  • J. Kamimoto (1998) On an integral of Hardy and Littlewood, Kyushu J. Math. 52 (1), pp. 249–263.
  • D. Kaminski and R. B. Paris (1999) On the zeroes of the Pearcey integral, J. Comput. Appl. Math. 107 (1), pp. 31–52.
  • E. Kamke (1977) Differentialgleichungen: Lösungsmethoden und Lösungen. Teil I, B. G. Teubner, Stuttgart (German).
  • M. Kaneko (1997) Poly-Bernoulli numbers, J. Théor. Nombres Bordeaux 9 (1), pp. 221–228.
  • E. Kanzieper (2002) Replica field theories, Painlevé transcendents, and exact correlation functions, Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).
  • 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.
  • 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).
  • 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).
  • A. A. Kapaev (2004) Quasi-linear Stokes phenomenon for the Painlevé first equation, J. Phys. A 37 (46), pp. 11149–11167.
  • N. S. Kapany and J. J. Burke (1972) Optical Waveguides, Quantum Electronics - Principles and Applications, Academic Press, New York.
  • 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.
  • 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.
  • E. L. Kaplan (1948) Auxiliary table for the incomplete elliptic integrals, J. Math. Physics 27, pp. 11–36.
  • A. A. Karatsuba and S. M. Voronin (1992) The Riemann Zeta-Function, de Gruyter Expositions in Mathematics, Vol. 5, Walter de Gruyter & Co., Berlin.
  • S. Karlin and J. L. McGregor (1961) The Hahn polynomials, formulas and an application, Scripta Math. 26, pp. 33–46.
  • 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.
  • 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.
  • K. A. Karpov and È. A. Čistova (1964) Tablitsy funktsii Vebera. Tom II, Vičisl. Centr Akad. Nauk SSSR, Moscow (Russian).
  • K. A. Karpov and È. A. Čistova (1968) Tablitsy funktsii Vebera. Tom III, Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
  • 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).
  • 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.
  • C. Kassel (1995) Quantum Groups, Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.
  • N. M. Katz (1975) The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers, Math. Ann. 216 (1), pp. 1–4.
  • E. H. Kaufman and T. D. Lenker (1986) Linear convergence and the bisection algorithm, Amer. Math. Monthly 93 (1), pp. 48–51.
  • A. Ya. Kazakov and S. Yu. Slavyanov (1996) Integral equations for special functions of Heun class, Methods Appl. Anal. 3 (4), pp. 447–456.
  • N. D. Kazarinoff (1988) Special functions and the Bieberbach conjecture, Amer. Math. Monthly 95 (8), pp. 689–696.
  • 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.
  • 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.
  • 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.
  • 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.
  • R. P. Kelisky (1957) On formulas involving both the Bernoulli and Fibonacci numbers, Scripta Math. 23, pp. 27–35.
  • 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.
  • 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.
  • M. K. Kerimov and S. L. Skorokhodov (1984c) Evaluation of complex zeros of Bessel functions Jν(z) and Iν(z) and their derivatives, Zh. Vychisl. Mat. i Mat. Fiz. 24 (10), pp. 1497–1513.
  • 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).
  • 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.
  • M. K. Kerimov and S. L. Skorokhodov (1985c) Calculation of the multiple zeros of the derivatives of the cylindrical Bessel functions Jν(z) and Yν(z), Zh. Vychisl. Mat. i Mat. Fiz. 25 (12), pp. 1749–1760, 1918.
  • 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).
  • 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.
  • 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).
  • 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.
  • M. K. Kerimov (1999) The Rayleigh function: Theory and computational methods, Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.
  • 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.
  • M. Kerker (1969) The Scattering of Light and Other Electromagnetic Radiation, Academic Press, New York.
  • A. D. Kerr (1978) An indirect method for evaluating certain infinite integrals, Z. Angew. Math. Phys. 29 (3), pp. 380–386.
  • 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.
  • D. Kershaw (1983) Some extensions of W. Gautschi’s inequalities for the gamma function, Math. Comp. 41 (164), pp. 607–611.
  • S. Kesavan and A. S. Vasudevamurthy (1985) On some boundary element methods for the heat equation, Numer. Math. 46 (1), pp. 101–120.
  • 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).
  • A. Khare, A. Lakshminarayan and U. Sukhatme (2003) Cyclic identities for Jacobi elliptic and related functions, J. Math. Phys. 44 (4), pp. 1822–1841.
  • A. Khare and U. Sukhatme (2002) Cyclic identities involving Jacobi elliptic functions, J. Math. Phys. 43 (7), pp. 3798–3806.
  • A. Khare and U. Sukhatme (2004) Connecting Jacobi elliptic functions with different modulus parameters, Pramana 63 (5), pp. 921–936.
  • A. I. Kheyfits (2004) Closed-form representations of the Lambert W function, Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
  • S. F. Khwaja and A. B. Olde Daalhuis (2012) Uniform asymptotic approximations for the Meixner-Sobolev polynomials, Anal. Appl. (Singap.) 10 (3), pp. 345–361.
  • H. Ki and Y. Kim (2000) On the zeros of some generalized hypergeometric functions, J. Math. Anal. Appl. 243 (2), pp. 249–260.
  • S. Kida (1981) A vortex filament moving without change of form, J. Fluid Mech. 112, pp. 397–409.
  • S. K. Kim (1972) The asymptotic expansion of a hypergeometric function F22(1,α;ρ1,ρ2;z), Math. Comp. 26 (120), pp. 963.
  • T. Kim and H. S. Kim (1999) Remark on p-adic q-Bernoulli numbers, Adv. Stud. Contemp. Math. (Pusan) 1, pp. 127–136.
  • N. Kimura (1988) On the degree of an irreducible factor of the Bernoulli polynomials, Acta Arith. 50 (3), pp. 243–249.
  • 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..
  • 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.
  • 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..
  • I. Ye. Kireyeva and K. A. Karpov (1961) Tables of Weber functions. Vol. I, Mathematical Tables Series, Vol. 15, Pergamon Press, London-New York.
  • A. N. Kirillov (1995) Dilogarithm identities, Progr. Theoret. Phys. Suppl. (118), pp. 61–142.
  • 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.
  • E. T. Kirkpatrick (1960) Tables of values of the modified Mathieu functions, Math. Comp. 14, pp. 118–129.
  • 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.
  • 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.
  • 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).
  • A. V. Kitaev (1994) Elliptic asymptotics of the first and second Painlevé transcendents, Uspekhi Mat. Nauk 49 (1(295)), pp. 77–140 (Russian).
  • Y. Kivshar and B. Luther-Davies (1998) Dark optical solitons: Physics and applications, Physics Reports 298 (2-3), pp. 81–197.
  • F. Klein (1894) Vorlesungen über die hypergeometrische Funktion, Göttingen (German).
  • 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).
  • H. Kneser (1950) Reelle analytische Lösungen der Gleichung φ(φ(x))=ex und verwandter Funktionalgleichungen, J. Reine Angew. Math. 187, pp. 56–67.
  • K. Knopp (1948) Theory and Application of Infinite Series, 2nd edition, Hafner, New York.
  • K. Knopp (1964) Theorie und Anwendung der unendlichen Reihen, 4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).
  • U. J. Knottnerus (1960) Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters, J. B. Wolters, Groningen.
  • D. E. Knuth and T. J. Buckholtz (1967) Computation of tangent, Euler, and Bernoulli numbers, Math. Comp. 21 (100), pp. 663–688.
  • 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.
  • D. E. Knuth (1986) METAFONT: The Program, Computers and Typesetting, Vol. D, Addison-Wesley, Reading, MA.
  • D. E. Knuth (1992) Two notes on notation, Amer. Math. Monthly 99 (5), pp. 403–422.
  • D. E. Knuth (1993) The Stanford GraphBase, ACM Press, New York.
  • N. Koblitz (1984) p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd edition, Graduate Texts in Mathematics, Vol. 58, Springer-Verlag, New York.
  • N. Koblitz (1993) Introduction to Elliptic Curves and Modular Forms, 2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.
  • N. Koblitz (1999) Algebraic Aspects of Cryptography, Springer-Verlag, Berlin.
  • 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.
  • M. Koecher (1954) Zur Theorie der Modulformen n-ten Grades. I, Math. Z. 59, pp. 399–416 (German).
  • 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.
  • R. Koekoek and R. F. Swarttouw (1998) The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Technical report Technical Report 98-17, Delft University of Technology, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics.
  • R. Koekoek, P. A. Lesky and R. F. Swarttouw (2010) Hypergeometric Orthogonal Polynomials and Their q-Analogues, Springer Monographs in Mathematics, Springer-Verlag, Berlin.
  • 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.
  • P. Koev and A. Edelman (2006) The efficient evaluation of the hypergeometric function of a matrix argument, Math. Comp. 75 (254), pp. 833–846.
  • 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.
  • S. Koizumi (1976) Theta relations and projective normality of Abelian varieties, Amer. J. Math. 98 (4), pp. 865–889.
  • 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.
  • C. G. Kokologiannaki, P. D. Siafarikas and C. B. Kouris (1992) On the complex zeros of Hμ(z), Jμ(z), Jμ′′(z) for real or complex order, J. Comput. Appl. Math. 40 (3), pp. 337–344.
  • G. A. Kolesnik (1969) An improvement of the remainder term in the divisor problem, Mat. Zametki 6, pp. 545–554 (Russian).
  • I. V. Komarov, L. I. Ponomarev and S. Yu. Slavyanov (1976) Sferoidalnye i kulonovskie sferoidalnye funktsii, Izdat. “Nauka”, Moscow (Russian).
  • E. Konishi (1996) Calculation of complex polygamma functions, Sci. Rep. Hirosaki Univ. 43 (1), pp. 161–183.
  • E. J. Konopinski (1981) Electromagnetic Fields and Relativistic Particles, International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.
  • T. H. Koornwinder (2012) Askey-Wilson polynomial, Scholarpedia 7 (7), pp. 7761.
  • T. H. Koornwinder and I. Sprinkhuizen-Kuyper (1978) Hypergeometric functions of 2×2 matrix argument are expressible in terms of Appel’s functions F4, Proc. Amer. Math. Soc. 70 (1), pp. 39–42.
  • 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.
  • T. H. Koornwinder (1975b) Jacobi polynomials. III. An analytic proof of the addition formula, SIAM. J. Math. Anal. 6, pp. 533–543.
  • T. H. Koornwinder (1975c) Two-variable Analogues of the Classical Orthogonal Polynomials, in Theory and Application of Special Functions, pp. 435–495.
  • T. H. Koornwinder (1977) The addition formula for Laguerre polynomials, SIAM J. Math. Anal. 8 (3), pp. 535–540.
  • T. H. Koornwinder (1984a) Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups, in Special Functions: Group Theoretical Aspects and Applications, pp. 1–85.
  • T. H. Koornwinder (1984b) Orthogonal polynomials with weight function (1-x)α(1+x)β+Mδ(x+1)+Nδ(x-1), Canad. Math. Bull. 27 (2), pp. 205–214.
  • T. H. Koornwinder (1989) Meixner-Pollaczek polynomials and the Heisenberg algebra, J. Math. Phys. 30 (4), pp. 767–769.
  • 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.
  • 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.
  • T. H. Koornwinder (2009) The Askey scheme as a four-manifold with corners, Ramanujan J. 20 (3), pp. 409–439.
  • Koornwinder (Web Site) Tom Koornwinder’s Personal Collection of Maple Procedures.
  • B. G. Korenev (2002) Bessel Functions and their Applications, Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
  • V. E. Korepin, N. M. Bogoliubov and A. G. Izergin (1993) Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, Cambridge.
  • N. M. Korobov (1958) Estimates of trigonometric sums and their applications, Uspehi Mat. Nauk 13 (4 (82)), pp. 185–192 (Russian).
  • S. Koumandos and M. Lamprecht (2010) Some completely monotonic functions of positive order, Math. Comp. 79 (271), pp. 1697–1707.
  • V. Kourganoff (1952) Basic Methods in Transfer Problems. Radiative Equilibrium and Neutron Diffusion, Oxford University Press, Oxford.
  • J. J. Kovacic (1986) An algorithm for solving second order linear homogeneous differential equations, J. Symbolic Comput. 2 (1), pp. 3–43.
  • 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).
  • 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.
  • 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.
  • Y. A. Kravtsov (1964) Asymptotic solution of Maxwell’s equations near caustics, Izv. Vuz. Radiofiz. 7, pp. 1049–1056.
  • Y. A. Kravtsov (1968) Two new asymptotic methods in the theory of wave propagation in inhomogeneous media, Sov. Phys. Acoust. 14, pp. 1–17.
  • Y. A. Kravtsov (1988) Rays and caustics as physical objects, in Progress in Optics, Vol. 26, pp. 227–348.
  • 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).
  • E. Kreyszig (1957) On the zeros of the Fresnel integrals, Canad. J. Math. 9, pp. 118–131.
  • I. M. Krichever (1976) An algebraic-geometrical construction of the Zakharov-Shabat equations and their periodic solutions, Sov. Math. Doklady 17, pp. 394–397.
  • 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).
  • 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.
  • S. G. Krivoshlykov (1994) Quantum-Theoretical Formalism for Inhomogeneous Graded-Index Waveguides, Akademie Verlag, Berlin-New York.
  • E. D. Krupnikov and K. S. Kölbig (1997) Some special cases of the generalized hypergeometric function Fqq+1, J. Comput. Appl. Math. 78 (1), pp. 79–95.
  • 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.
  • 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.
  • V. I. Krylov and N. S. Skoblya (1985) A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation, Mir, Moscow.
  • H. Kuki (1972) Algorithm 421. Complex gamma function with error control, Comm. ACM 15 (4), pp. 271–272.
  • M. Kurz (1979) Fehlerabschätzungen zu asymptotischen Entwicklungen der Eigenwerte und Eigenlösungen der Mathieuschen Differentialgleichung, Ph.D. Thesis, Universität Duisburg-Essen, Essen, D 45177.
  • V. B. Kuznetsov and S. Sahi (Eds.) (2006) Jack, Hall-Littlewood and Macdonald Polynomials, Contemporary Mathematics, Vol. 417, American Mathematical Society, Providence, RI.
  • V. B. Kuznetsov (1992) Equivalence of two graphical calculi, J. Phys. A 25 (22), pp. 6005–6026.
  • 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.
  • 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.
  • K. S. Kölbig (1968) Algorithm 327: Dilogarithm [S22], Comm. ACM 11 (4), pp. 270–271.
  • 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.
  • K. S. Kölbig (1972a) Complex zeros of two incomplete Riemann zeta functions, Math. Comp. 26 (118), pp. 551–565.
  • K. S. Kölbig (1972b) On the zeros of the incomplete gamma function, Math. Comp. 26 (119), pp. 751–755.
  • 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.
  • K. S. Kölbig (1981) A program for computing the conical functions of the first kind P-12+iτm(x) for m=0 and m=1, Comput. Phys. Comm. 23 (1), pp. 51–61.
  • K. S. Kölbig (1986) Nielsen’s generalized polylogarithms, SIAM J. Math. Anal. 17 (5), pp. 1232–1258.
  • T. W. Körner (1989) Fourier Analysis, 2nd edition, Cambridge University Press, Cambridge.