Elliott's identity and hypergeometric functions

Balasubramanian, R. ; Naik, S. ; Ponnusamy, S. ; Vuorinen, M. (2002) Elliott's identity and hypergeometric functions Journal of Mathematical Analysis and Applications, 271 (1). pp. 232-256. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0022-247X(02)00126-9


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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Legendre's Relation; Elliott's Identity; Hypergeometric Functions
ID Code:72365
Deposited On:29 Nov 2011 12:45
Last Modified:29 Nov 2011 12:45

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