DUALITY AND RECIPROCITY FOR HYPERGEOMETRIC SERIES WITH A GAMMA PRODUCT FORMULA
- 1 January 2019
- journal article
- research article
- Published by Faculty of Mathematics, Kyushu University in Kyushu Journal of Mathematics
- Vol. 73 (2), 251-294
- https://doi.org/10.2206/kyushujm.73.251
Abstract
Following a previous article we continue our study on non-terminating hypergeometric series with one free parameter, which aims to find arithmetical constraints for a given hypergeometric series to admit a gamma product formula. In this article we exploit the concepts of duality and reciprocity not only to extend already obtained results to a larger region but also to strengthen themselves substantially. Among other things we are able to settle the rationality and finiteness conjectures posed in the previous article.Keywords
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