Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
type: Item
instance of: scholarly article
title: Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
zbMATH Open document ID: 0855.33012
DOI: 10.1016/0898-1221(96)00114-9
publication date: 1996-12-19T00:00:00Z
review text: Using a simple method, numerous summation formulas for hypergeometric and basic hypergeometric series are derived. Among these summation formulas are nonterminating extensions and \(q\)-extensions of identities recorded by Lavoie, Luke, Watson, and Srivastava. At the result side of the basic hypergeometric summations, there appears a \(q\)-analogue of the digamma function. Some of its properties are also studied. Various special and limit cases of the results presented in this paper are discussed.
Mathematics Subject Classification ID: 33D20
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 950629
zbMATH Keywords: summation formulas
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: \(q\)-digamma function
zbMATH Keywords: \(q\)-polygamma function
author: C. Krattenthaler
author: H. M. Srivastava
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00114-9
OpenAlex ID: W2032988465
cites work: Some remarks on uniform asymptotic expansions for Bessel functions
cites work: Some Evaluations for the Generalized Hypergeometric Series
cites work: Some Summation Formulas for the Series 3 F 2 (1)
cites work: A Simple Algorithm for the Evaluation of a Class of Generalized Hypergeometric Series
cites work: Q4040884
cites work: Q4760447
cites work: Q5508372
cites work: Theq-Gamma andq-Beta Functions†
cites work: The \(q\)-gamma function for \(q>1\)
cites work: The q-gamma function for \(x<0\)
cites work: Some Summation Formulae for Nonterminating Basic Hypergeometric Series
cites work: Ramanujan's Extensions of the Gamma and Beta Functions
cites work: Completely monotonic functions associated with the gamma function and its q-analogues
cites work: Q3209423
cites work: Q3952397
cites work: Q5820721
cites work: Q3844537
published in: Computers & Mathematics with Applications
Recommended article: Q5144274
Recommended article: Closed-form summations of certain hypergeometric-type series containing the digamma function
Recommended article: Summations for certain series containing the digamma function
Recommended article: Sums of certain double q-hypergeometric series
Recommended article: A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
Recommended article: Q3575331
Recommended article: Q5041392
Recommended article: Q5526241
Recommended article: Q4287248
description: scientific article; zbMATH DE number 950629