asymptotic%20expansions%20of%20integrals
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1—10 of 22 matching pages
1: 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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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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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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2: Bibliography S
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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A simple approach to asymptotic expansions for Fourier integrals of singular functions.
Appl. Math. Comput. 216 (11), pp. 3378–3385.
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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels.
SIAM J. Math. Anal. 11 (5), pp. 828–841.
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Uniform asymptotic expansions of Hermite polynomials.
M. Phil. thesis, City University of Hong Kong.
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3: 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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Asymptotic expansions for the zeros of certain special functions.
J. Comput. Appl. Math. 145 (2), pp. 261–267.
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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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4: 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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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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An asymptotic expansion of the double gamma function.
J. Approx. Theory 111 (2), pp. 298–314.
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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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5: Bibliography V
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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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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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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6: 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 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, exponentially improved, asymptotic expansions for the generalized exponential integral.
SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
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Uniform, exponentially improved, asymptotic expansions for the confluent hypergeometric function and other integral transforms.
SIAM J. Math. Anal. 22 (5), pp. 1475–1489.
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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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7: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
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Olver (1960) tabulates , , , , , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as ; see §10.21(viii), and more fully Olver (1954).
Zhang and Jin (1996, p. 270) tabulates , , , , , 8D.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Zhang and Jin (1996, p. 271) tabulates , , , , , 8D.
Olver (1960) tabulates , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as .
9: Bibliography C
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Asymptotic expansion of the first elliptic integral.
SIAM J. Math. Anal. 16 (5), pp. 1072–1092.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point.
Proc. Roy. Soc. London Ser. A 426, pp. 273–286.
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Remarks on the full asymptotic expansion of Feynman parametrized integrals.
Lett. Nuovo Cimento (2) 13 (8), pp. 310–312.
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On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
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10: 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 approximations for the first incomplete elliptic integral near logarithmic singularity.
J. Comput. Appl. Math. 205 (1), pp. 186–206.
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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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The asymptotic expansion of a hypergeometric function
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Math. Comp. 26 (120), pp. 963.
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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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