Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the con-fluent hypergeometric function by using their integral representa-tions and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the above-mentioned extended functions and investigating various formulas for the further extended functions in a systematic manner. More-over, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.