Eisenstein%20series
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21—30 of 333 matching pages
21: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Special Functions, -Series and Related Topics.
Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.
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-Series from a Contemporary Perspective.
Contemporary Mathematics, Vol. 254, American Mathematical Society, Providence, RI.
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Quantum Field Theory.
International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.
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22: 12.20 Approximations
§12.20 Approximations
►Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions and (§13.2(i)) whose regions of validity include intervals with endpoints and , respectively. As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …23: 16.20 Integrals and Series
§16.20 Integrals and Series
… ►Series of the Meijer -function are given in Erdélyi et al. (1953a, §5.5.1), Luke (1975, §5.8), and Prudnikov et al. (1990, §6.11). …24: 8 Incomplete Gamma and Related
Functions
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25: 28 Mathieu Functions and Hill’s Equation
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26: 4.33 Maclaurin Series and Laurent Series
§4.33 Maclaurin Series and Laurent Series
…27: 12.18 Methods of Computation
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►These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions.
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28: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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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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29: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Integrals of Airy Functions.
National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
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Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors.
2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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30: Bibliography O
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Summing one- and two-dimensional series related to the Euler series.
J. Comput. Appl. Math. 98 (2), pp. 245–271.
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Inverse factorial-series solutions of difference equations.
Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations.
Methods Appl. Anal. 1 (1), pp. 1–13.
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The Generalized Exponential Integral.
In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.),
International Series of Numerical Mathematics, Vol. 119, pp. 497–510.
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