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 |
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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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