asymptotic expansions for large parameters
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21: Bibliography L
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Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
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22: 13.21 Uniform Asymptotic Approximations for Large
§13.21 Uniform Asymptotic Approximations for Large
… ►This reference also includes error bounds and extensions to asymptotic expansions and complex values of . … ►§13.21(iv) Large , Other Expansions
… ►For asymptotic expansions having double asymptotic properties see Skovgaard (1966). … ►23: 12.16 Mathematical Applications
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►In Brazel et al. (1992) exponential asymptotics are considered in connection with an eigenvalue problem involving PCFs.
►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
…Integral transforms and sampling expansions are considered in Jerri (1982).
24: Bibliography W
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An asymptotic expansion of with large variable and parameters.
Math. Comp. 27 (122), pp. 429–436.
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25: 28.26 Asymptotic Approximations for Large
§28.26 Asymptotic Approximations for Large
►§28.26(i) Goldstein’s Expansions
… ►The asymptotic expansions of and in the same circumstances are also given by the right-hand sides of (28.26.4) and (28.26.5), respectively. … ►§28.26(ii) Uniform Approximations
… ►For asymptotic approximations for see also Naylor (1984, 1987, 1989).26: 13.19 Asymptotic Expansions for Large Argument
§13.19 Asymptotic Expansions for Large Argument
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13.19.3
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►Error bounds and exponentially-improved expansions are derivable by combining §§13.7(ii) and 13.7(iii) with (13.14.2) and (13.14.3).
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►For an asymptotic expansion of as that is valid in the sector and where the real parameters
, are subject to the growth conditions , , see Wong (1973a).
27: 28.16 Asymptotic Expansions for Large
28: 10.40 Asymptotic Expansions for Large Argument
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10.40.2
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29: 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
…30: 10.41 Asymptotic Expansions for Large Order
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10.41.4
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