Fox–Wright function

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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 an idea of E. Maitland Wright (1935):

Its normalisation

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):


  • Wright, E. M. (1935). "The asymptotic expansion of the generalized hypergeometric function". Proc. London Math. Soc. 10 (4): 286–293. doi:10.1112/jlms/s1-10.40.286. 
  • 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.