# 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.

## Key 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}.