Ratios of the Gauss hypergeometric functions with parameters shifted by integers: more on integral representations
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.03595
 arXiv:
 arXiv:2108.03595
 Bibcode:
 2021arXiv210803595D
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 33C05;
 30B70;
 47B50
 EPrint:
 16 pages