A1 Refereed original research article in a scientific journal
Elliott's identity and hypergeometric functions
Authors: Balasubramanian R., Naik S., Ponnusamy S., Vuorinen M.
Publication year: 2002
Journal:: Journal of Mathematical Analysis and Applications
Journal name in source: Journal of Mathematical Analysis and Applications
Volume: 271
Issue: 1
First page : 232
Last page: 256
Number of pages: 25
ISSN: 0022-247X
DOI: https://doi.org/10.1016/S0022-247X(02)00126-9
Web address : http://api.elsevier.com/content/abstract/scopus_id:0036660231
Abstract
Elliott's identity involving the Gaussian hypergeometric series contains, as a special case, the classical Legendre identity for 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 Elliott's identity and which also leads to concavity/convexity properties of certain related functions. We also show that Elliott's identity is equivalent to a formula of Ramanujan on the differentiation of quotients of hypergeometric functions. Applying these results we obtain a number of identities associated with the Legendre functions of the first and the second kinds, respectively. © 2002 Elsevier Science (USA). All rights reserved.
Elliott's identity involving the Gaussian hypergeometric series contains, as a special case, the classical Legendre identity for 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 Elliott's identity and which also leads to concavity/convexity properties of certain related functions. We also show that Elliott's identity is equivalent to a formula of Ramanujan on the differentiation of quotients of hypergeometric functions. Applying these results we obtain a number of identities associated with the Legendre functions of the first and the second kinds, respectively. © 2002 Elsevier Science (USA). All rights reserved.
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