A1 Refereed original research article in a scientific journal
Functional Inequalities for the Quotients of Hypergeometric Functions
Authors: Balasubramanian R., Ponnusamy S., Vuorinen M.
Publication year: 1998
Journal:: Journal of Mathematical Analysis and Applications
Journal name in source: Journal of Mathematical Analysis and Applications
Volume: 218
Issue: 1
First page : 256
Last page: 268
Number of pages: 13
ISSN: 0022-247X
DOI: https://doi.org/10.1006/jmaa.1997.5776
Web address : http://api.elsevier.com/content/abstract/scopus_id:0010786092
Abstract
LetF(a,b;c;x) be the Gaussian hypergeometric series and for 0<1 let[formula]G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen raised recently the following problem: For whicha,b∈(0,1) does[formula]hold for allr,s∈(0,1)? They also proved this inequality fora=b=1/2. The main purpose of this paper is to give an answer to this problem fora+b=1 and to find a lower bound for the summ(r)+m(s) fora∈(0,2) andb∈(0,2-a]. © 1998 Academic Press.
LetF(a,b;c;x) be the Gaussian hypergeometric series and for 0<1 let[formula]G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen raised recently the following problem: For whicha,b∈(0,1) does[formula]hold for allr,s∈(0,1)? They also proved this inequality fora=b=1/2. The main purpose of this paper is to give an answer to this problem fora+b=1 and to find a lower bound for the summ(r)+m(s) fora∈(0,2) andb∈(0,2-a]. © 1998 Academic Press.
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