GENERALIZED S-FUNCTION AND ITS APPLICATION TO STATISTICAL DISTRIBUTION

In this paper, we present p + q + m and p + q + 2m parametric S-functions, exploring therelationships between these two types of functions. We derive their fundamental properties, including gener-ating functions, recurrence relations, differential formulas and integral representations. From these results, weestablish several notable corollaries. Furthermore, we present a distribution function involving the S-functionand compute the Laplace transform of its density function. Additionally, we explore the connections betweenthe S-function and other significant transcendental functions