Contiguous relations of $_3\phi_2$-series

TL;DR

This paper derives many contiguous relations for $_3\phi_2$-series using Abel's lemma and linear combinations, serving as q-analogues of known relations for $_3F_2$-series, expanding the theoretical framework of basic hypergeometric functions.

Contribution

It introduces new contiguous relations for $_3\phi_2$-series as q-analogues of classical $_3F_2$ relations, employing Abel's lemma and linear combination techniques.

Findings

Established numerous contiguous relations for $_3\phi_2$-series.

Connected q-analogues to classical hypergeometric series relations.

Enhanced the theoretical understanding of basic hypergeometric functions.

Abstract

According to Abel's lemma and the method of linear combinations, we establish numerous contiguous relations of $_3\phi_2$-series, which can be regarded as q-analogues of the contiguous relations of $_3F_2$-series due to Krattenthaler and Rivoal [12] or Chu and Wang [4].