On Integral Relations of Incomplete Aleph-functions and Applications

Integral Relations of Incomplete Aleph-functions

Abstract

Aleph ($\aleph $)-functions are very general and advanced types of mathematical functions used in many areas. Over time, they have been extended in different ways, one of which is the incomplete Aleph-function. In this paper, we find integral relations for incomplete Aleph-functions and use them to solve double integrals that involve Bessel functions, hypergeometric functions, and incomplete Aleph-functions. We show that these double integrals can be solved more easily when certain known results are used. The results we present are quite general, and we also give some specific examples to show how they work in special cases.