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11: 2.7 Differential Equations
All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients. …
12: Bibliography M
  • H. Maass (1971) Siegel’s modular forms and Dirichlet series. Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.
  • G. F. Miller (1966) On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation. SIAM J. Numer. Anal. 3 (3), pp. 390–409.
  • P. J. Mohr and B. N. Taylor (2005) CODATA recommended values of the fundamental physical constants: 2002. Rev. Mod.Phys. 77, pp. 1–107.
  • L. J. Mordell (1958) On the evaluation of some multiple series. J. London Math. Soc. (2) 33, pp. 368–371.
  • C. Mortici (2011a) A new Stirling series as continued fraction. Numer. Algorithms 56 (1), pp. 17–26.
  • 13: Bibliography T
  • A. Takemura (1984) Zonal Polynomials. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 4, Institute of Mathematical Statistics, Hayward, CA.
  • I. C. Tang (1969) Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.
  • J. G. Taylor (1978) Error bounds for the Liouville-Green approximation to initial-value problems. Z. Angew. Math. Mech. 58 (12), pp. 529–537.
  • J. G. Taylor (1982) Improved error bounds for the Liouville-Green (or WKB) approximation. J. Math. Anal. Appl. 85 (1), pp. 79–89.
  • G. P. Tolstov (1962) Fourier Series. Prentice-Hall Inc., Englewood Cliffs, N.J..
  • 14: 25.11 Hurwitz Zeta Function
    25.11.10 ζ ( s , a ) = n = 0 ( s ) n n ! ζ ( n + s ) ( 1 a ) n , s 1 , | a 1 | < 1 .
    15: Bibliography H
  • P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
  • M. H. Halley, D. Delande, and K. T. Taylor (1993) The combination of R -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.
  • G. H. Hardy (1912) Note on Dr. Vacca’s series for γ . Quart. J. Math. 43, pp. 215–216.
  • G. H. Hardy (1949) Divergent Series. Clarendon Press, Oxford.
  • E. Hille (1929) Note on some hypergeometric series of higher order. J. London Math. Soc. 4, pp. 50–54.
  • 16: 12.13 Sums
    §12.13(ii) Other Series
    For other series see Dhar (1940), Hansen (1975, pp. 421–422), Hillion (1997), Miller (1974), Prudnikov et al. (1986b, p. 651), Shanker (1940b, a, c), and Varma (1941).
    17: Bibliography K
  • 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.
  • 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.
  • E. J. Konopinski (1981) Electromagnetic Fields and Relativistic Particles. International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.
  • B. G. Korenev (2002) Bessel Functions and their Applications. Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
  • 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.
  • 18: Bibliography B
  • W. N. Bailey (1928) Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
  • W. N. Bailey (1929) Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
  • W. N. Bailey (1964) Generalized Hypergeometric Series. Stechert-Hafner, Inc., New York.
  • K. A. Berrington, P. G. Burke, J. J. Chang., A. T. Chivers, W. D. Robb, and K. T. Taylor (1974) A general program to calculate atomic continuum processes using the R-matrix method. Comput. Phys. Comm. 8 (3), pp. 149–198.
  • W. Bühring (1987a) An analytic continuation of the hypergeometric series. SIAM J. Math. Anal. 18 (3), pp. 884–889.