Representations and inequalities for generalized hypergeometric functions
Classical Analysis and ODEs
2014-09-11 v1
Abstract
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this representation we establish various new facts regarding generalized hypergeometric functions, including complete monotonicity, log-convexity in upper parameters, monotonicity of ratios and new proofs of Luke's bounds. Besides, we derive two-sided inequalities for the Bessel type hypergeometric functions by using their series representations.
Cite
@article{arxiv.1409.3071,
title = {Representations and inequalities for generalized hypergeometric functions},
author = {Dmitrii Karp},
journal= {arXiv preprint arXiv:1409.3071},
year = {2014}
}
Comments
13 pages, no figures