On the Very-well-poised Bilateral Basic Hypergeometric $_5\psi_5$ Series

TL;DR

This paper establishes new transformation formulas for the very-well-poised bilateral basic hypergeometric $_5\psi_5$ series by relating it to $_8\phi_7$ series, advancing the understanding of hypergeometric series transformations.

Contribution

It introduces novel transformation formulas for $_5\psi_5$ series using their connection to $_8\phi_7$ series, expanding the toolkit for hypergeometric series analysis.

Findings

Derived several transformation formulas for $_5\psi_5$ series.

Linked bilateral $_5\psi_5$ series to $_8\phi_7$ series.

Enhanced methods for manipulating hypergeometric series.

Abstract

In this paper, we prove several transformation formulas for the very-well-poised bilateral basic hypergeometric $_5\psi_5$ series by using the relationship between the bilateral basic hypergeometric $_5\psi_5$ series and basic hypergeometric $_8\phi_7$ series.