Transformation formulas and three-term relations for basic hypergeometric series

TL;DR

This paper generalizes Gasper's transformation formulas for basic hypergeometric series and provides explicit coefficients for three-term relations, extending previous results in the field.

Contribution

The paper introduces two new generalized transformation formulas and explicit three-term relation coefficients for {}_{2}phi_{1} series, advancing the understanding of hypergeometric series relations.

Findings

Generalized Gasper's transformation formulas

Explicit coefficients for three-term relations for {}_{2}phi_{1}

Extension of previous results on hypergeometric series

Abstract

We derive two generalizations of Gasper's transformation formula for basic hypergeometric series. Using these generalized formulas, we give explicit expressions for the coefficients of three-term relations for the basic hypergeometric series {}_{2}phi_{1}, which are generalizations of the author's previous results on three-term relations for {}_{2}phi_{1}.