Hypergeometric identities for 10 extended Ramanujan-type series

TL;DR

This paper uses the WZ-method to prove hypergeometric identities that connect ten extended Ramanujan-type series to simpler series, valid for all convergent parameter values and as limits in some cases.

Contribution

It introduces new hypergeometric identities relating extended Ramanujan series to simpler series, expanding the understanding of these mathematical structures.

Findings

Proved identities valid for all convergent parameter values

Established identities as limits when series do not converge

Connected ten extended Ramanujan-type series to simpler hypergeometric series

Abstract

We prove, by the WZ-method, some hypergeometric identities which relate ten extended Ramanujan type series to simpler hypergeometric series. The identities we are going to prove are valid for all the values of a parameter $a$ when they are convergent. Sometimes, even if they do not converge, they are valid if we consider these identities as limits.