Whittaker’s equation-based formulation of a new class of analytic functions combined with geometric analysis

Abstract

A special function is a function with a particular use in mathematical physics or another branch of mathematics and is often named after an early scientist who researched its characteristics. A few noteworthy instances exist, such as the hypergeometric function and its distinct species. By using k-calculus, this sort of special function is made more generic. K-symbol calculus is utilized in this study to develop the k-convoluted operators associated with the k-Whittaker function (confluent hypergeometric function of the first kind). Through the use of this recently created operator, we propose a new geometric formula of normalized functions in the unit disk. Our strategy is to modify the theory of differential subordination, thus we geometrically investigate the most well-known characteristics of this new operator, including subordination features and coefficient bounds. We draw attention to some notable corollaries of our main conclusions as exceptional examples.