• CERTAIN TRANSFORMATION BASIC AND POLY-BASIC HYPERGEOMETRIC SERIES

Abstract

In this work, new transformations of fundamental and poly-fundamental hypergeometric series were established using the Bailey lemma. Using Bailey's transform and known sums of partial series, specific transformations of poly-basic hypergeometric series have been tried. There are some established transformations of basic multi-base hypergeometric series. Some of them connect two products from the Q-series. The bi-basic and poly-basic q-series are altered in some really fascinating ways as a result of these discoveries.