Functional Inequalities for the Quotients of Hypergeometric Functions

: Balasubramanian R., Ponnusamy S., Vuorinen M.

: 1998

Journal of Mathematical Analysis and Applications

: Journal of Mathematical Analysis and Applications

: 218

: 1

: 256

: 268

: 13

: 0022-247X

DOI: https://doi.org/10.1006/jmaa.1997.5776

: http://api.elsevier.com/content/abstract/scopus_id:0010786092

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.