Generalization and extension of Beta function is presented. In addition, a new generalization of the beta function with three and four parameters k, m, n and r are introduced. This new beta function gives upto 4! derivative of new function including Eulerís beta function and generalized beta function. The objective of this generalization and extension of beta function is to extend the domain of intersection of beta and gamma function.
Keywords: Special function; Beta function; Gamma function; Generalized; Extended