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Bibliography K

  • 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), A. Iserles and M. J. D. Powell (Eds.), 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, N.J..
  • 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.
  • A. Kalähne (1907) Über die Wurzeln einiger Zylinderfunktionen und gewisser aus ihnen gebildeter Gleichungen. Zeitschrift für Mathematik und Physik 54, pp. 55–86 (German).
  • 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.
  • G. A. Kalugin and D. J. Jeffrey (2011) Unimodal sequences show that Lambert W is Bernstein. C. R. Math. Acad. Sci. Soc. R. Can. 33 (2), pp. 50–56.
  • G. A. Kalugin, D. J. Jeffrey, and R. M. Corless (2012) Bernstein, Pick, Poisson and related integral expressions for Lambert W. Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
  • 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.
  • R. P. Kanwal (1983) Generalized functions. Mathematics in Science and Engineering, Vol. 171, Academic Press, Inc., Orlando, FL.
  • 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.
  • M. Katsurada (2003) Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.
  • 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, J. P. Keating, 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.
  • S. F. Khwaja and A. B. Olde Daalhuis (2013) Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.
  • 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.
  • Y. S. Kim, A. K. Rathie, and R. B. Paris (2013) An extension of Saalschütz’s summation theorem for the series Fr+2r+3. Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
  • 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.