A Study of certain Special Functions: Generalizations, Recursion Formulas and Derivatives with respect to Parameters of certain Special Functions

The theory of special functions constitutes an important branch of mathematics. Functions of particular interest are called special functions. By tradition, these are the functions which appear frequently enough in applications to merit independent study (the gamma function, the Riemann zeta function, Bessel functions, and so on). A more refined viewpoint is to consider special functions as solutions of differential, difference or functional equations of certain types. The subject of special functions has been continuously developed, with contributions by a host of mathematicians, including Euler, Legendre, Gauss, Kummer, Riemann and Ramanujan. A renewed interest in multivariable hypergeometric functions took place from the 1980's that reflected developments in the fields of geometry, representation theory and mathematical physics. This book contains generalization of hypergeometric series resulting from generalizing the Pochhammer symbol; recursion formulas for certain generalized multivariable hypergeometric functions and Derivatives of certain multivariable hypergeometric functions and multivariable q-hypergeometric functions with respect to their parameters.