Functional inequalities for the quotients of hypergeometric functions

Balasubramanian, R. ; Ponnusamy, S. ; Vuorinen, M. (1998) Functional inequalities for the quotients of hypergeometric functions Journal of Mathematical Analysis and Applications, 218 (1). pp. 256-268. ISSN 0022-247X

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

Related URL: http://dx.doi.org/10.1006/jmaa.1997.5776

Abstract

Let F(a, b; c; x) be the Gaussian hypergeometric series and for 0 < r< 1 let[formula]G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen raised recently the following problem: For which a, b ∈ (0, 1) does[formula]hold for all r, s ∈ (0, 1)? They also proved this inequality for a = b = 1/2. The main purpose of this paper is to give an answer to this problem for a + b = 1 and to find a lower bound for the summ(r) + m(s) fora ∈ (0, 2) and b ∈ (0, 2 − a].

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