Ratios of the Gauss hypergeometric functions with parameters shifted by integers: more on integral representations
Classical Analysis and ODEs
2021-12-30 v1
Abstract
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for this ratio based on a formula for its imaginary part. This work extends our recent results by lifting certain restrictions on parameters. The new representations are illustrated with a few examples and an application to products of ratios.
Keywords
Cite
@article{arxiv.2108.03595,
title = {Ratios of the Gauss hypergeometric functions with parameters shifted by integers: more on integral representations},
author = {Alexander Dyachenko and Dmitrii Karp},
journal= {arXiv preprint arXiv:2108.03595},
year = {2021}
}
Comments
16 pages; nofigures