Double series and relations with hypergeometric functions

In this thesis, double series identities were examined and their consequences involving hypergeometric functions in one or more variables were investigated.To do this, the quadratic transformations, cubic transformations or summation theorems were applied to double series firstly. Then, the identities that given for double series were reduced to series in one variable with the help of Srivastava-Daoust hypergeometric function. Finally, the associated generating function relations were given by using the identities that obtained for a class of polynomial.Keywords: Double series, Hypergeometric functions, Hypergeometric polynomials, Generating functions