Generalizations of Andrews' curious identities

TL;DR

This paper extends Andrews' curious q-series identities by introducing two generalized formulas with an extra parameter, leading to new extensions of classical hypergeometric series identities and related results.

Contribution

The paper presents novel generalizations of Andrews' identities using series rearrangement, adding an extra integer parameter to broaden their applicability.

Findings

Two new generalized q-series identities established.

Extensions of Andrews' $_3F_2(3/4)$-series identities derived.

Several related identities and results provided.

Abstract

According to the method of series rearrangement, we establish two generalizations of Andrews' curious $q$-series identity with an extra integer parameter. The limiting cases of them produce two extensions of Andrews' curious $_3F_2(\frac{3}{4})$-series identity with an additional integer parameter. Meanwhile, several related results are also given.