A Study of Summation Identities for Basic Hypergeometric and Mock Theta Functions

Abstract

In the present Work, newlineMaking use of concept splitting the limits of summation identities and Bailey s lemma, an attempt has been to establish the transformations involving Bailey s lemma and Truncated Basic Hypergeometric Series. newline newlineThe Bailey s Lemma is very powerful appliance to generate summation identities for Basic Hypergeometric Functions and Truncated Basic Bilateral Hypergeometric Function. A number of summation identities involving Truncated Basic Bilateral Hypergeometric Functions have been establish through the Mechanism of symmetric Bailey s Lemma. newline newlineThe very interesting functions introduced by S. Ramanujan to G. H. Hardy in his last article, which is mock theta function unlike false theta function. The various relation and transformations for mock theta function and infinite product analogues to the identities of Ramanujan, established using well known identities. newline newlineand#61558; An attempt has been made to generate certain transformation formulae involving various transform. newline newlineIn this paper, we have established certain Results involving ratio of summation and continued fractions. newline