# Several transformation formulas involving bilateral basic hypergeometric series

## TL;DR

This paper proves three new transformation formulas for bilateral basic hypergeometric series using analytic continuation, including a result equivalent to Jouhet's involving $_8 heta_8$ and $_8 ext{phi}_7$ series.

## Contribution

It introduces three novel transformation formulas for bilateral basic hypergeometric series, expanding the theoretical framework of hypergeometric series transformations.

## Key findings

- Proved three new transformation formulas for bilateral basic hypergeometric series
- One formula is equivalent to Jouhet's result involving $_8 heta_8$ and $_8 ext{phi}_7$ series
- Enhanced understanding of hypergeometric series transformations

## Abstract

In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result involving two $_8\psi_8$ series and two $_8\phi_7$ series.