GENERALIZED S-FUNCTION AND ITS APPLICATION TO STATISTICAL DISTRIBUTION
Abstract
In this paper, we present p+q+m and p+q+2m parametric S-functions,
exploring the relationships between these two types of functions. We derive their fundamental
properties, including generating functions, recurrence relations, differential
formulas and integral representations. From these results, we establish several notable
corollaries. Furthermore, we present a distribution function involving the S-function
and compute the Laplace transform of its density function. Additionally, we explore
the connections between the S-function and other significant transcendental functions.
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