Abel's method on summation by parts and theta hypergeometric series
type: Item
instance of: scholarly article
title: Abel's method on summation by parts and theta hypergeometric series
zbMATH Open document ID: 1154.33008
author: Cangzhi Jia
author: Wenchang Chu
published in: Journal of Combinatorial Theory. Series A
publication date: 2008-09-04T00:00:00Z
review text: This paper deals with summation formulae of terminating theta hypergeometric series. The authors develop an iterating machinery for evaluating such series. By employing this technique they present most of the known theta hypergeometric series identities, but they also find several new transformation and summation formulae. The authors give a brief introduction to theta hypergeometric series, then they present the iterating machinery including a modified Abel lemma on summation by parts. By means of this lemma the authors review most of the known theta hypergeometric series identities and discover several new theta summation formulae.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 5321399
zbMATH Keywords: Abel's lemma on summation by parts
zbMATH Keywords: modified Jacobi theta function
zbMATH Keywords: Weierstrass' three-term relation
zbMATH Keywords: theta (elliptic) hypergeometric series
zbMATH Keywords: fundamental Frenkel-Turaev identity
zbMATH Keywords: Bailey's transformation on terminating very-well-poised \(_{10}{}_\phi{}_9{}\)-series
MaRDI profile type: Publication
full work available at URL: j.jcta.2007.11.002
OpenAlex ID: W1980909730
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DOI: 10.1016/J.JCTA.2007.11.002
description: scientific article; zbMATH DE number 5321399