Some Identities Involving Hypergeometric Functions

This paper focuses on formulating and proving some identities involving hypergeometric functions. The main result generalizes an identity previously proven for specific cases, specifically for $m=1$ and $m=2$ with $b=a-1$. To prove the primary identity, the Laplace transform method is employed. The mathematical proof also utilizes the notations introduced by Srivastava and Daoust, as well as the properties of the Kampé de Fériet function. Additionally, a second identity is formulated and presented. These generalized identities can be actively applied to analyze and solve various boundary-value problems in the theory of differential equations.