# Some new Transformations for Bailey pairs and WP-Bailey Pairs

## TL;DR

This paper introduces new transformations connecting WP-Bailey pairs and standard Bailey pairs, leading to general expansions for theta function products and Lambert series.

## Contribution

It presents novel transformations for WP-Bailey pairs and their relation to standard Bailey pairs, enabling broader expansions of theta functions.

## Key findings

- Derived new transformations for WP-Bailey pairs
- Established connections to standard Bailey pairs
- Produced general expansions for theta functions and Lambert series

## Abstract

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.