asymptotic%20expansion
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11—20 of 27 matching pages
11: 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
… ►12: Bibliography B
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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order.
SIAM J. Appl. Math. 15, pp. 1315–1323.
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Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions.
Expo. Math. 2 (4), pp. 289–347.
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Asymptotic Expansions of Integrals.
Holt, Rinehart, and Winston, New York.
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Uniform asymptotic expansion of Charlier polynomials.
Methods Appl. Anal. 1 (3), pp. 294–313.
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On the asymptotic expansion of some integrals.
Arch. Math. (Basel) 42 (3), pp. 253–259.
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13: Bibliography F
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On the reversion of an asymptotic expansion and the zeros of the Airy functions.
SIAM Rev. 41 (4), pp. 762–773.
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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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An asymptotic expansion of the double gamma function.
J. Approx. Theory 111 (2), pp. 298–314.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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14: 30.9 Asymptotic Approximations and Expansions
§30.9 Asymptotic Approximations and Expansions
… ►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). … ►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: 28.8 Asymptotic Expansions for Large
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28.8.1
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16: Bibliography W
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Asymptotic expansions for second-order linear difference equations with a turning point.
Numer. Math. 94 (1), pp. 147–194.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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Asymptotic expansions of the Kontorovich-Lebedev transform.
Appl. Anal. 12 (3), pp. 161–172.
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Applications of some recent results in asymptotic expansions.
Congr. Numer. 37, pp. 145–182.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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17: 11.6 Asymptotic Expansions
§11.6 Asymptotic Expansions
►§11.6(i) Large , Fixed
… ►§11.6(ii) Large , Fixed
… ►More fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions (§2.1(v)). …18: Bibliography M
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Asymptotic expansions for the zeros of certain special functions.
J. Comput. Appl. Math. 145 (2), pp. 261–267.
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Explicit error terms for asymptotic expansions of Stieltjes transforms.
J. Inst. Math. Appl. 22 (2), pp. 129–145.
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Exact remainders for asymptotic expansions of fractional integrals.
J. Inst. Math. Appl. 24 (2), pp. 139–147.
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Asymptotic expansion of a multiple integral.
SIAM J. Math. Anal. 18 (6), pp. 1630–1637.
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On asymptotic expansions of ellipsoidal wave functions.
Math. Nachr. 32, pp. 157–172.
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19: Bibliography V
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Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
J. Math. Anal. Appl. 269 (1), pp. 317–331.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Asymptotic expansion of the generalized hypergeometric function as for
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Anal. Appl. (Singap.) 21 (2), pp. 535–545.
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20: Bibliography O
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Asymptotic expansions for -gamma, -exponential, and -Bessel functions.
J. Math. Anal. Appl. 186 (3), pp. 896–913.
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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function.
Methods Appl. Anal. 5 (4), pp. 425–438.
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On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles.
Methods Appl. Anal. 7 (4), pp. 727–745.
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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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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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