Fox–Wright function

In mathematics, the Fox–Wright function (also known as Fox–Wright Psi function or just Wright function, not to be confused with Wright Omega function) is a generalisation of the generalised hypergeometric function pFq(z) based on ideas of Charles Fox (1928) and E. Maitland Wright (1935):

Upon changing the normalisation

it becomes pFq(z) for A1...p = B1...q = 1.

The Fox–Wright function is a special case of the Fox H-function (Srivastava & Manocha 1984, p. 50):

References

  • Fox, C. (1928). "The asymptotic expansion of integral functions defined by generalized hypergeometric series". Proc. London Math. Soc. 27 (1): 389–400. doi:10.1112/plms/s2-27.1.389.
  • Wright, E. M. (1935). "The asymptotic expansion of the generalized hypergeometric function". J. London Math. Soc. 10 (4): 286–293. doi:10.1112/jlms/s1-10.40.286.
  • Wright, E. M. (1940). "The asymptotic expansion of the generalized hypergeometric function". Proc. London Math. Soc. 46 (2): 389–408. doi:10.1112/plms/s2-46.1.389.
  • Wright, E. M. (1952). "Erratum to "The asymptotic expansion of the generalized hypergeometric function"". J. London Math. Soc. 27: 254. doi:10.1112/plms/s2-54.3.254-s.
  • Srivastava, H.M.; Manocha, H.L. (1984). A treatise on generating functions. ISBN 0-470-20010-3.
  • Miller, A. R.; Moskowitz, I.S. (1995). "Reduction of a Class of Fox–Wright Psi Functions for Certain Rational Parameters". Computers Math. Applic. 30 (11): 73–82. doi:10.1016/0898-1221(95)00165-u.
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