Uniformly convergent expansions for the generalized hypergeometric functions p–1Fp and pFp. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: López, José L.; Pagola, Pedro J.; Karp, Dmitrii B.
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 10(2020)
• Page Start: 820
• Page End: 837
• Publication Date: 2020-10-02
• Subjects: Generalized hypergeometric function -- Bessel function -- Kummer function -- convergent expansions -- uniform expansions; 33C20 -- 41A58 -- 41A80; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1752687
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We derive a convergent expansion of the generalized hypergeometric function p − 1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We further obtain a convergent expansion of the generalized hypergeometric function p F p in terms of the confluent hypergeometric functions 1 F 1 that holds uniformly in any right half-plane. For both functions, we make a further step forward and give convergent expansions in terms of trigonometric, exponential and rational functions that hold uniformly in the same domains. For all four expansions we present explicit error bounds. The accuracy of the approximations is illustrated by some numerical experiments.