Expansion formulas for multiple basic hypergeometric series over root systems

TL;DR

This paper generalizes expansion formulas for multiple basic hypergeometric series over root systems, expanding their applicability in special functions and number theory through advanced transformation and summation techniques.

Contribution

It extends Liu's formulas to multiple series over root systems and incorporates transformations from Wang and Ma using $q$-Lagrange inversion and Bailey transformations.

Findings

Extended Liu's expansion formulas to root systems

Applied Bailey transformations to derive new identities

Enhanced tools for special functions and number theory

Abstract

We extend expansion formulas of Liu given in 2013 to the context of multiple series over root systems. Liu and others have shown the usefulness of these formulas in Special Functions and number-theoretic contexts. We extend Wang and Ma's generalizations of Liu's work which they obtained using $q$-Lagrange inversion. We use the $A_n$ and $C_n$ Bailey transformation and other summation theorems due to Gustafson, Milne, Milne and Lilly, and others, from the theory of $A_n$, $C_n$ and $D_n$ basic hypergeometric series.