On Ramanujan asymptotic expansions and inequalities for hypergeometric functions

Balasubramanian, R. ; Ponnusamy, S. (1998) On Ramanujan asymptotic expansions and inequalities for hypergeometric functions Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 108 (2). pp. 95-108. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/108/2/95-10...

Related URL: http://dx.doi.org/10.1007/BF02841543

Abstract

In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functions F(a,b;c;x), c ≤ a + b, near the singularity x = 1. Further, we obtain monotonous properties of the quotient of two hypergeometric functions and inequalities for certain combinations of them. Finally, we also solve an open problem of finding conditions on a, b > 0 such that 2F(−a,b;a + b;r2) < (2−r2)F(a,b;a + b;r2) holds for all r∈(0,1).

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Hypergeometric Functions; Gamma Function; Elliptic Integrals
ID Code:1312
Deposited On:04 Oct 2010 07:52
Last Modified:16 May 2016 12:27

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