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1: 13.8 Asymptotic Approximations for Large Parameters
§13.8(ii) Large b and z , Fixed a and b / z
2: 8.18 Asymptotic Expansions of I x ( a , b )
§8.18(ii) Large Parameters: Uniform Asymptotic Expansions
3: 8.12 Uniform Asymptotic Expansions for Large Parameter
§8.12 Uniform Asymptotic Expansions for Large Parameter
Inverse Function
4: Bibliography O
  • A. B. Olde Daalhuis (2003a) Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.
  • A. B. Olde Daalhuis (2003b) Uniform asymptotic expansions for hypergeometric functions with large parameters. II. Analysis and Applications (Singapore) 1 (1), pp. 121–128.
  • A. B. Olde Daalhuis (2010) Uniform asymptotic expansions for hypergeometric functions with large parameters. III. Analysis and Applications (Singapore) 8 (2), pp. 199–210.
  • F. W. J. Olver (1980b) Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
  • 5: 13.20 Uniform Asymptotic Approximations for Large μ
    §13.20(i) Large μ , Fixed κ
    6: 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
    7: 28.8 Asymptotic Expansions for Large q
    §28.8 Asymptotic Expansions for Large q
    Barrett’s Expansions
    The approximations apply when the parameters a and q are real and large, and are uniform with respect to various regions in the z -plane. …
    Dunster’s Approximations
    8: 13.21 Uniform Asymptotic Approximations for Large κ
    §13.21 Uniform Asymptotic Approximations for Large κ
    9: 28.26 Asymptotic Approximations for Large q
    §28.26 Asymptotic Approximations for Large q
    §28.26(ii) Uniform Approximations
    10: 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