Certain bilateral generating relations for generalized hypergeometric functions
type: Item
instance of: scholarly article
title: Certain bilateral generating relations for generalized hypergeometric functions
zbMATH Open document ID: 0853.33011
DOI: 10.1007/BF02837197
author: Maya Lahiri
author: B. Satyanarayana
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-09-24T00:00:00Z
review text: In this short note the authors have given bilateral generating relations (in the form of a single result) for the generalized hypergeometric functions \(I^{\alpha; (a_p)}_{n; (b_q)} (x,w)\), defined by \[ I^{\alpha; (a_p)}_{n; (b_q)} (x,w) = {1 \over n! (x - w)^{[\alpha_w]}} \Delta^n_{x,w} \left[ (x - w)^{\bigl[ (\alpha + n) w \bigr]} _{p + 1} F_q \left( (a_p), - {x \over w}; (b_q); w \right) \right] \] where, \[ \Delta_{x,w} f(x) = {f(x + w) - f(x) \over w}. \] To establish their result they used series manipulation technique. The result involves generalized Lauricella hypergeometric functions of four variables and is too lengthy to be reproduced here.
Mathematics Subject Classification ID: 33C50
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 903365
zbMATH Keywords: difference operator
zbMATH Keywords: bilateral generating relations
zbMATH Keywords: Lauricella hypergeometric function of four variables
reviewed by: Hukum Chand Agrawal
MaRDI profile type: Publication
cites work: Biorthogonal polynomials suggested by the Laguerre polynomials
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description: scientific article; zbMATH DE number 903365