Log-convexity and log-concavity of hypergeometric-like functions

Details Log-convexity and log-concavity of hypergeometric-like functions Log-convexity and log-concavity of hypergeometric-like functions

2009-02-18

arxiv.org/abs/0902.3073v1

Mathematics

Classical Analysis and ODEs

13 pages, no figures

Scientific paper

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms $a\mapsto\sum{f_k}(a)_kx^k$, $a\mapsto\sum{f_k}\Gamma(a+k)x^k$ and $a\mapsto\sum{f_k}x^k/(a)_k$. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Tur\'{a}n inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexity results for the same function recently proved by Baricz. Besides, we establish a reverse inequality which complements naturally the inequality of Barnard, Gordy and Richards. Similar results are established for the Gauss and the generalized hypergeometric functions. A conjecture about monotonicity of a quotient of products of confluent hypergeometric functions is made.

Affiliated with

Also associated with

No associations

Rating

Log-convexity and log-concavity of hypergeometric-like functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Log-convexity and log-concavity of hypergeometric-like functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Log-convexity and log-concavity of hypergeometric-like functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127959