Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation

TL;DR

This paper explores multiple hypergeometric transformation formulas derived from the balanced duality transformation, including generalizations of classical identities, through symmetry and limiting processes.

Contribution

It introduces new transformation formulas for $A_n$ basic hypergeometric series based on the balanced duality transformation and its symmetries.

Findings

Derived new transformation formulas for hypergeometric series.

Generalized Watson, Sears, and ${}_8 W_7$ transformations.

Connected different dimensions through limiting processes.

Abstract

Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking certain limits of the balanced duality transformation. By combining some of them, some transformation formulas for $A_n$ basic hypergeometric series is given. They include some generalizations of Watson, Sears and ${}_8 W_7$ transformations.