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uniform asymptotic expansions for large parameter

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1: 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
2: 8.12 Uniform Asymptotic Expansions for Large Parameter
§8.12 Uniform Asymptotic Expansions for Large Parameter
Inverse Function
3: 8.18 Asymptotic Expansions of I x ( a , b )
§8.18(ii) Large Parameters: Uniform Asymptotic Expansions
4: 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
5: 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).

  • 6: 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.
  • 7: Bibliography F
  • S. Farid Khwaja and A. B. Olde Daalhuis (2014) Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.
  • J. L. Fields (1973) Uniform asymptotic expansions of certain classes of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.
  • J. L. Fields (1983) Uniform asymptotic expansions of a class of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
  • 8: 28.8 Asymptotic Expansions for Large q
    §28.8 Asymptotic Expansions for Large q
    Barrett’s Expansions
    9: Bibliography D
  • T. M. Dunster (1986) Uniform asymptotic expansions for prolate spheroidal functions with large parameters. SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
  • 10: 13.21 Uniform Asymptotic Approximations for Large κ
    §13.21 Uniform Asymptotic Approximations for Large κ
    §13.21(iv) Large κ , Other Expansions
    For a uniform asymptotic expansion in terms of Airy functions for W κ , μ ( 4 κ x ) when κ is large and positive, μ is real with | μ | bounded, and x [ δ , ) see Olver (1997b, Chapter 11, Ex. 7.3). … For asymptotic expansions having double asymptotic properties see Skovgaard (1966). …