Extensions of classical hypergeometric identities of Bailey and Whipple
Abstract
We obtain extensions of classical hypergeometric identities of Bailey and Whipple that transform nearly-poised and very-well-poised series to Saalsch\"utzian series, Saalsch\"utzian series to Saalsch\"utzian series, and very-well-poised and nearly-poised series to very-well-poised series. We employ a method in which summations and transformations of lower-order series are used to obtain transformations of higher-order series. By taking limits, we also obtain extensions of two classical quadratic transformations of Whipple and Bailey. Furthermore, we show how a number of other well-known results regarding hypergeometric series follow as special cases of our results.
Keywords
Cite
@article{arxiv.2006.15616,
title = {Extensions of classical hypergeometric identities of Bailey and Whipple},
author = {Ilia D. Mishev},
journal= {arXiv preprint arXiv:2006.15616},
year = {2020}
}
Comments
25 pages, a section containing extensions of classical quadratic transformations has been added