Dr. Ritika
Mathematic
September 2022
Hypergeometric functions are taken into account in the theory of special functions, in which case the representations of the functions will be hypergeometric series. The special function theory has historically been used extensively in many fields of mathematical physics, economics, statistics, engineering, and many other scientific disciplines. This work is focused on the investigation of the k-analogue of Gauss hypergeometric functions by the Hadamard product, which was inspired by some recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions. Additionally, this function yields convergence features. A unique function utilised in mathematics is the Gaussian function, commonly referred to as the common hypergeometric function. The hypergeometric series, which also includes numerous other special functions as specific or limiting examples, serves as a representation of this function. It is the linear solution of a second-order ordinary differential equation (ODE). Any linear ODE of the second order with three regular singular points can be transformed using this equation. In this research, we talk about the invention of a few basic hypergeometric functions. Understanding the importance of the collection of hypergeometric functions in various domains is the goal of this work. This paper's emphasis is on providing background knowledge. New, previously unpublished equations that are cohesively weaved into the body of current mathematical literature make up a large amount of the content.
351- 361
© Airo Journals 2021
