A New Extension of Combination of Linear and Bilinear Generating Relations in Function Spaces Associated with Hypergeometric Polynomials; Some New Applications of Two Signals in Special Functions

For a certain class of generalized hypergeometric polynomials, the first derive some special cases on linear and bilinear generating functions and then apply these generating functions in order to reduce the corresponding results for the classical Jacobi, Hermite, Laguerre and Gegenbauer Polynomials, hypergeometric functions of Gauss and functions of Bessel and Kelvin. They also consider several linear generating functions for these polynomials as well as for some multivariable Jacobi and multivariable Laguerre polynomials which were investigated in recent years. Some of the linear and bilinear generating functions, presented in this paper, are associated with the hypergeometric polynomials.