On incomplete Gamma and Beta integrals

Abstract

This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio arising in comparing the mean differences among groups is obtained as an application.

This is the third of the series of articles: arXiv:2601.21304; arXiv:2410.14490; arXiv:2505.00470