asymptotic approximations for large parameters
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1: 13.8 Asymptotic Approximations for Large Parameters
§13.8 Asymptotic Approximations for Large Parameters
… ►§13.8(ii) Large and , Fixed and
… ►§13.8(iii) Large
… ► … ►§13.8(iv) Large and
…2: 28.26 Asymptotic Approximations for Large
3: 28.8 Asymptotic Expansions for Large
4: 13.20 Uniform Asymptotic Approximations for Large
5: 13.21 Uniform Asymptotic Approximations for Large
§13.21 Uniform Asymptotic Approximations for Large
… ►6: 8.12 Uniform Asymptotic Expansions for Large Parameter
7: 2.4 Contour Integrals
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§2.4(i) Watson’s Lemma
… ►Then … ►For examples see Olver (1997b, pp. 315–320). ►§2.4(iii) Laplace’s Method
… ►§2.4(v) Coalescing Saddle Points: Chester, Friedman, and Ursell’s Method
…8: 2.3 Integrals of a Real Variable
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►Then
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►For the Fourier integral
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►Then the series obtained by substituting (2.3.7) into (2.3.1) and integrating formally term by term yields an asymptotic expansion:
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►(In other words, differentiation of (2.3.8) with respect to the parameter
(or ) is legitimate.)
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►