Landen inequalities for zero-balanced hypergeometric functions

Details Landen inequalities for zero-balanced hypergeometric functions Landen inequalities for zero-balanced hypergeometric functions

2011-10-30

arxiv.org/abs/1110.6619v1

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

For zero-balanced Gaussian hypergeometric functions $ F(a,b;a+b;x),$ $a,b>0,$
we determine maximal regions of $ab$ plane where well-known Landen identities
for the complete elliptic integral of the first kind turn on respective
inequalities valid for each $x\in (0,1)$. Thereby an exhausting answer is given
to an open problem.

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