Abstract:

Generating functions are presented here in their general form for the first time. Use of the generating function allows us to derive the terms of various polynomials. Moreover, we determine the nth term, an n, of the polynomial. When solving issues in physics, engineering, statistics, and operations research, special functions—and specifically hypergeometric functions and polynomials in one or more variables—are commonly needed. Several writers have recently paid attention to generation functions, summations, and transformations formula in the theory of special functions. The study of special functions relies heavily on generating functions, finite sum characteristics, and transformations. In light of the increasing relevance of generating functions, this dissertation includes specific classes of generating functions, including linear, bilinear, bilateral, double, and multiple generating functions for selected special functions and polynomials in one, two, or more variables. You can get these generating functions by utilising the series rearrangement method, integral operator approaches, Nishimoto's fractional calculus, or group theoretic methods.

Description:

Special Function, Equation, Generating function, Sciences, Application