Elliott's identity and hypergeometric functions
type: Item
instance of: scholarly article
title: Elliott's identity and hypergeometric functions
zbMATH Open document ID: 1011.33010
DOI: 10.1016/S0022-247X(02)00126-9
author: R. Balasubramanian
author: Saminathan Ponnusamy
author: Swatee Naik
author: M. Vuorinen
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: Elliot's identity involving the Gaussian hypergeometric series contains, as a special case, the classical Legendre identity for the complete elliptic integrals. The aim of this paper is to derive a differentiation formula for an expression involving the Gaussian hypergeometric series, which, for appropriate values of the parameters, implies Elliot's identity and which also leads to concavity/convexity properties of certain related functions. The authors also show that Elliot's identity is equivalent to a formula of Ramanujan on the differentiation of quotients of hypergeometric functions. Applying these results the authors obtain a number of identities associated with the Legendre functions of the first and the second kind, respectively.
reviewed by: W. Koepf
Mathematics Subject Classification ID: 33C99
zbMATH DE Number: 1836750
zbMATH Keywords: Elliot's identity
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: complete elliptic integrals
zbMATH Keywords: Legendre functions of the second kind
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1836750