On hypergeometric functions and generalizations of Legendre's relation

: Karatsuba E., Vuorinen M.

: 2001

: Journal of Mathematical Analysis and Applications

: 260

: 2

: 623

: 640

: 18

: 0022-247X

DOI: https://doi.org/10.1006/jmaa.2001.7499

: http://api.elsevier.com/content/abstract/scopus_id:0035882848

We prove some convexity properties for a sum of hypergeometric functions and obtain a generalization of Legendre's relation for complete elliptic integrals. We apply these results to prove some inequalities for hypergeometric functions, incomplete beta-functions, and Legendre functions. © 2001 Academic Press.