On hypergeometric functions and generalizations of Legendre's relation

Authors
Karatsuba, EA Vuorinen, M
Citation
Ea. Karatsuba et M. Vuorinen, On hypergeometric functions and generalizations of Legendre's relation, J MATH ANAL, 260(2), 2001, pp. 623-640
Citations number
8
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
260
Issue
2
Year of publication
2001
Pages
623 - 640
Database
ISI
SICI code
0022-247X(20010805)260:2<623:OHFAGO>2.0.ZU;2-7
Abstract
We prove some convexity properties for a sum of hypergeometric functions an d obtain a generalization of Legendre's relation for complete elliptic inte grals. We apply these results to prove some inequalities for hypergeometric functions, incomplete beta-functions, and Legendre functions. (C) 2001 Aca demic Press.