asymptotic%20expansions%20for%20large%20order
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1—10 of 13 matching pages
1: Bibliography D
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Asymptotic Expansions: Their Derivation and Interpretation.
Academic Press, London-New York.
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On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function.
Methods Appl. Anal. 5 (3), pp. 223–247.
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Uniform asymptotic expansions for prolate spheroidal functions with large parameters.
SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Uniform asymptotic expansions for associated Legendre functions of large order.
Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
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2: 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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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order.
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
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Some new asymptotic expansions for Bessel functions of large orders.
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
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The asymptotic expansion of Bessel functions of large order.
Philos. Trans. Roy. Soc. London. Ser. A. 247, pp. 328–368.
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Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders.
J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
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3: 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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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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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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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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4: 28.8 Asymptotic Expansions for Large
§28.8 Asymptotic Expansions for Large
… ►§28.8(ii) Sips’ Expansions
… ►§28.8(iii) Goldstein’s Expansions
… ►Barrett’s Expansions
… ►5: Bibliography N
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The resurgence properties of the large order asymptotics of the Anger-Weber function I.
J. Class. Anal. 4 (1), pp. 1–39.
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The resurgence properties of the large order asymptotics of the Anger-Weber function II.
J. Class. Anal. 4 (2), pp. 121–147.
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On the large argument asymptotics of the Lommel function via Stieltjes transforms.
Asymptot. Anal. 91 (3-4), pp. 265–281.
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Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions.
Acta Appl. Math. 150, pp. 141–177.
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Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions.
Stud. Appl. Math. 140 (4), pp. 508–541.
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6: 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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Anharmonic oscillator. II. A study of perturbation theory in large order.
Phys. Rev. D 7, pp. 1620–1636.
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Unfolding the high orders of asymptotic expansions with coalescing saddles: Singularity theory, crossover and duality.
Proc. Roy. Soc. London Ser. A 443, pp. 107–126.
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Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation.
J. Phys. A 30 (2), pp. 559–571.
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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
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7: 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)). …8: 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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Asymptotic expansions for second-order linear difference equations. II.
Stud. Appl. Math. 87 (4), pp. 289–324.
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Asymptotic expansions for second-order linear difference equations.
J. Comput. Appl. Math. 41 (1-2), pp. 65–94.
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An asymptotic expansion of with large variable and parameters.
Math. Comp. 27 (122), pp. 429–436.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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9: 12.11 Zeros
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§12.11(ii) Asymptotic Expansions of Large Zeros
… ►When the zeros are asymptotically given by and , where is a large positive integer and … ►§12.11(iii) Asymptotic Expansions for Large Parameter
►For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). For example, let the th real zeros of and , counted in descending order away from the point , be denoted by and , respectively. …10: Bibliography C
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Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial as the index and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials.
Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
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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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On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
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Asymptotic Expansions.
Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.
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