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asymptotic expansions for large parameter

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1: 8.20 Asymptotic Expansions of E p ( z )
§8.20(ii) Large p
2: 8.18 Asymptotic Expansions of I x ( a , b )
§8.18(ii) Large Parameters: Uniform Asymptotic Expansions
Symmetric Case
General Case
Inverse Function
3: 12.11 Zeros
§12.11(iii) Asymptotic Expansions for Large Parameter
4: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10(vi) Modifications of Expansions in Elementary Functions
Modified Expansions
5: 8.12 Uniform Asymptotic Expansions for Large Parameter
§8.12 Uniform Asymptotic Expansions for Large Parameter
Inverse Function
6: 16.22 Asymptotic Expansions
For asymptotic expansions of Meijer G -functions with large parameters see Fields (1973, 1983).
7: 12.14 The Function W ( a , x )
§12.14(ix) Uniform Asymptotic Expansions for Large Parameter
Positive a , 2 a < x <
Airy-type Uniform Expansions
8: 16.11 Asymptotic Expansions
§16.11(iii) Expansions for Large Parameters
9: 14.32 Methods of Computation
  • Application of the uniform asymptotic expansions for large values of the parameters given in §§14.15 and 14.20(vii)14.20(ix).

  • 10: 2.3 Integrals of a Real Variable
    Then … Then the series obtained by substituting (2.3.7) into (2.3.1) and integrating formally term by term yields an asymptotic expansion: …