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11—20 of 38 matching pages
11: 11.6 Asymptotic Expansions
12: 26.10 Integer Partitions: Other Restrictions
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§26.10(ii) Generating Functions
… ►where the last right-hand side is the sum over of the generating functions for partitions into distinct parts with largest part equal to . … ►
26.10.5
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§26.10(vi) Bessel-Function Expansion
… ►where is the modified Bessel function (§10.25(ii)), and …13: 12.11 Zeros
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§12.11(i) Distribution of Real Zeros
… ►§12.11(ii) Asymptotic Expansions of Large Zeros
… ►§12.11(iii) Asymptotic Expansions for Large Parameter
… ►where is the function inverse to , defined by (12.10.39) (see also (12.10.41)), and … ►For further information, including associated functions, see Olver (1959).14: 30.9 Asymptotic Approximations and Expansions
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§30.9(i) Prolate Spheroidal Wave Functions
… ►For uniform asymptotic expansions in terms of Airy or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1986). … ►§30.9(ii) Oblate Spheroidal Wave Functions
… ►For uniform asymptotic expansions in terms of elementary, Airy, or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1992, 1995). … ►§30.9(iii) Other Approximations and Expansions
…15: Bibliography F
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Uniform asymptotic expansions for hypergeometric functions with large parameters IV.
Anal. Appl. (Singap.) 12 (6), pp. 667–710.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Uniform asymptotic expansions of certain classes of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 4 (3), pp. 482–507.
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Uniform asymptotic expansions of a class of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
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16: Bibliography O
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Uniform asymptotic expansions for hypergeometric functions with large parameters. I.
Analysis and Applications (Singapore) 1 (1), pp. 111–120.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. II.
Analysis and Applications (Singapore) 1 (1), pp. 121–128.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. III.
Analysis and Applications (Singapore) 8 (2), pp. 199–210.
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Legendre functions with both parameters large.
Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
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Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
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17: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions.
Comput. Phys. Comm. 178 (7), pp. 535–551.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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Tables of the functions of the parabolic cylinder for negative integer parameters.
Zastos. Mat. 13, pp. 261–273.
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18: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
… ► … ►Modified Expansions
… ►19: 3.8 Nonlinear Equations
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