Some Generalized Special Functions and their Properties

In the present paper, first, we investigate a generalized Pochhammer's symbol and its various properties in terms of a new symbol (s, k), where s, k > 0. Then, we define a generalization of gamma and beta functions and their various associated properties in the form of (s, k). Also, we define new generalization of hyperge-ometric functions and develop differential equations for generalized hypergeometric functions in the form of (s, k). We present that generalized hypergeometric functions are the solution of the said differential equa-tion. Furthermore, some useful results, properties and integral representation related to these generalized Pochhammer's symbol, gamma function, beta function, and hypergeometric functions are presented.