asymptotic approximations
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11: 28.26 Asymptotic Approximations for Large
§28.26 Asymptotic Approximations for Large
… ►§28.26(ii) Uniform Approximations
… ►For asymptotic approximations for see also Naylor (1984, 1987, 1989).12: 2.1 Definitions and Elementary Properties
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►means that for each , the difference between and the th partial sum on the right-hand side is as in .
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►Some asymptotic approximations are expressed in terms of two or more Poincaré asymptotic expansions.
…For an example see (2.8.15).
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§2.1(iv) Uniform Asymptotic Expansions
… ►§2.1(v) Generalized Asymptotic Expansions
…13: 15.12 Asymptotic Approximations
§15.12 Asymptotic Approximations
►§15.12(i) Large Variable
… ►§15.12(ii) Large
… ►As , … ►For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).14: 10.70 Zeros
15: 13.22 Zeros
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►Asymptotic approximations to the zeros when the parameters and/or are large can be found by reversion of the uniform approximations provided in §§13.20 and 13.21.
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16: 33.21 Asymptotic Approximations for Large
§33.21 Asymptotic Approximations for Large
►§33.21(i) Limiting Forms
… ►§33.21(ii) Asymptotic Expansions
…17: 35.9 Applications
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►The asymptotic approximations of §35.7(iv) are applied in numerous statistical contexts in Butler and Wood (2002).
►In chemistry, Wei and Eichinger (1993) expresses the probability density functions of macromolecules in terms of generalized hypergeometric functions of matrix argument, and develop asymptotic approximations for these density functions.
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18: Roderick S. C. Wong
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►He is the author of the book Asymptotic Approximations of Integrals, published by Academic Press in 1989 and reprinted by SIAM in its Classics in Applied Mathematics Series in 2001, and of Lecture Notes on Applied Analysis, published by World Scientific in 2010.
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