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in terms of parabolic cylinder functions

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1: 12.16 Mathematical Applications
2: 18.24 Hahn Class: Asymptotic Approximations
This expansion is in terms of the parabolic cylinder function and its derivative. … Both expansions are in terms of parabolic cylinder functions. … This expansion is uniformly valid in any compact x -interval on the real line and is in terms of parabolic cylinder functions. …
3: Bibliography O
  • 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.
  • 4: Bibliography L
  • T. A. Lowdon (1970) Integral representation of the Hankel function in terms of parabolic cylinder functions. Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.
  • 5: 32.10 Special Function Solutions
    P IV  has solutions expressible in terms of parabolic cylinder functions12.2) iff either …
    6: 12.10 Uniform Asymptotic Expansions for Large Parameter
    §12.10(ii) Negative a , 2 a < x <
    §12.10(vi) Modifications of Expansions in Elementary Functions
    §12.10(vii) Negative a , 2 a < x < . Expansions in Terms of Airy Functions
    Modified Expansions
    7: Bibliography C
  • T. M. Cherry (1948) Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.
  • 8: 12.14 The Function W ( a , x )
    Positive a , 2 a < x <
    Airy-type Uniform Expansions
    9: 2.8 Differential Equations with a Parameter
    For further examples of uniform asymptotic approximations in terms of parabolic cylinder functions see §§13.20(iii), 13.20(iv), 14.15(v), 15.12(iii), 18.24. …
    10: 16.18 Special Cases
    §16.18 Special Cases
    The F 1 1 and F 1 2 functions introduced in Chapters 13 and 15, as well as the more general F q p functions introduced in the present chapter, are all special cases of the Meijer G -function. …As a corollary, special cases of the F 1 1 and F 1 2 functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer G -function. Representations of special functions in terms of the Meijer G -function are given in Erdélyi et al. (1953a, §5.6), Luke (1969a, §§6.4–6.5), and Mathai (1993, §3.10).