Investigation of the k-Analogue of Gauss Hypergeometric Functions Constructed by the Hadamard Product

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and other branches science. Inspired by certain recent extensions k-analogue gamma, Pochhammer symbol, hypergeometric functions, this work is devoted to study Gauss functions Hadamard product. We give a definition product k-Gauss (HPkGHF) associated with fourth numerator two denominator parameters. In addition, convergence properties are derived from function. also discuss interesting such as derivative formulae, integral representations, transforms including beta transform Laplace transform. Furthermore, we investigate some contiguous relations differential equations connecting HPkGHF. The current results more general than previous ones. Moreover, proposed useful k-special where naturally occurs.