Beta-Function Identities via Probabilistic Approach

TL;DR

This paper introduces a probabilistic method to derive new identities involving beta functions, generalizing known combinatorial identities with binomial coefficients and gamma functions.

Contribution

It presents a novel probabilistic approach to establish identities involving beta functions, expanding the theoretical understanding of these mathematical relationships.

Findings

Derived new beta function identities using probabilistic methods

Generalized classical combinatorial identities involving gamma functions

Provided a framework connecting probability theory with special functions

Abstract

Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.