New Modified Gamma and Beta Functions with an Application

This note presents a novel set of modified Gamma and Beta k functions. The authors introduce these new functions along with their first and second summation relations, functional relations, symmetry relations, Mellin transforms, and integral representations that incorporate algebraic powers and Mittag-Leffler functions, as well as those involving trigonometric terms, powers, and Mittag-Leffler functions. In contrast to other studies that generalize Gamma and Beta functions, this note highlights a statistical application, demonstrating the practical utility of the proposed functions across various fields.