Taylor series
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11—18 of 18 matching pages
11: 2.7 Differential Equations
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►All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients.
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12: Bibliography M
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Siegel’s modular forms and Dirichlet series.
Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.
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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.
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CODATA recommended values of the fundamental physical constants: 2002.
Rev. Mod.Phys. 77, pp. 1–107.
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On the evaluation of some multiple series.
J. London Math. Soc. (2) 33, pp. 368–371.
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A new Stirling series as continued fraction.
Numer. Algorithms 56 (1), pp. 17–26.
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13: Bibliography T
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Zonal Polynomials.
Institute of Mathematical Statistics Lecture Notes—Monograph
Series, 4, Institute of Mathematical Statistics, Hayward, CA.
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Some definite integrals and Fourier series for Jacobian elliptic functions.
Z. Angew. Math. Mech. 49, pp. 95–96.
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Error bounds for the Liouville-Green approximation to initial-value problems.
Z. Angew. Math. Mech. 58 (12), pp. 529–537.
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Improved error bounds for the Liouville-Green (or WKB) approximation.
J. Math. Anal. Appl. 85 (1), pp. 79–89.
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Fourier Series.
Prentice-Hall Inc., Englewood Cliffs, N.J..
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14: 25.11 Hurwitz Zeta Function
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25.11.10
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15: Bibliography H
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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).
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The combination of -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr.
J. Phys. B 26 (12), pp. 1775–1790.
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Note on Dr. Vacca’s series for
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Quart. J. Math. 43, pp. 215–216.
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Divergent Series.
Clarendon Press, Oxford.
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Note on some hypergeometric series of higher order.
J. London Math. Soc. 4, pp. 50–54.
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16: 12.13 Sums
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§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
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Series expansions for the third incomplete elliptic integral via partial fraction decompositions.
J. Comput. Appl. Math. 207 (2), pp. 331–337.
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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Electromagnetic Fields and Relativistic Particles.
International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.
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Bessel Functions and their Applications.
Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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18: Bibliography B
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Products of generalized hypergeometric series.
Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
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Transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
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Generalized Hypergeometric Series.
Stechert-Hafner, Inc., New York.
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A general program to calculate atomic continuum processes using the R-matrix method.
Comput. Phys. Comm. 8 (3), pp. 149–198.
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An analytic continuation of the hypergeometric series.
SIAM J. Math. Anal. 18 (3), pp. 884–889.
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