A Study on Elliptic WP-Bailey Transformation for Hypergeometric Series

Abstract

Ramanujan studied hypergeometric series extensively before is gone to England. The chapter 12, 13 and 15 in the first
notebook deal with these series. There are many left hand pages in the first notebook that contain facts about
hypergeometric series and hypergeometric functions. When I try to understand Ramanujan’s impact on mathematics, it is
useful to see what was known when he started to work, to try to figure out what he knew, and then see what he
rediscovered or added to known mathematics. Making use of an elliptic WP-Bailey pair and certain theorems for
constructing elliptic WP-Bailey chains, I has established some transformation formulae for theta hypergeometric series.