uniform asymptotic approximation

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21: 8.12 Uniform Asymptotic Expansions for Large Parameter

§8.12 Uniform Asymptotic Expansions for Large Parameter

… ►For other uniform asymptotic approximations of the incomplete gamma functions in terms of the function $\mathrm{erfc}$ see Paris (2002b) and Dunster (1996a). ►

Inverse Function

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22: 13.20 Uniform Asymptotic Approximations for Large $\mu$

§13.20 Uniform Asymptotic Approximations for Large $\mu$

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§13.20(i) Large $\mu$, Fixed $\kappa$

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23: 10.57 Uniform Asymptotic Expansions for Large Order

§10.57 Uniform Asymptotic Expansions for Large Order

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24: 13.21 Uniform Asymptotic Approximations for Large $\kappa$

§13.21 Uniform Asymptotic Approximations for Large $\kappa$

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25: 13.8 Asymptotic Approximations for Large Parameters

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§13.8(ii) Large $b$ and $z$, Fixed $a$ and $b/z$

… ►Also, more complicated—but more powerful—uniform asymptotic approximations can be obtained by combining (13.14.4), (13.14.5) with §§13.20(iii) and 13.20(iv). … ► …

26: 35.7 Gaussian Hypergeometric Function of Matrix Argument

… ►Butler and Wood (2002) applies Laplace’s method (§2.3(iii)) to (35.7.5) to derive uniform asymptotic approximations for the functions …

27: 2.1 Definitions and Elementary Properties

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§2.1(iv) Uniform Asymptotic Expansions

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28: 10.21 Zeros

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§10.21(viii) Uniform Asymptotic Approximations for Large Order

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29: 10.69 Uniform Asymptotic Expansions for Large Order

§10.69 Uniform Asymptotic Expansions for Large Order

… ►All fractional powers take their principal values. ►All four expansions also enjoy the same kind of double asymptotic property described in §10.41(iv). … ►

30: Bibliography W

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On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.

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External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§8.11(v).

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