INVESTIGATING GENERALIZED HYPERGEOMETRIC FUNCTIONS AND THEIR RELATIONS WITH K-FUNCTIONS IN ONE AND TWO VARIABLES

Abstract

We explore the features and relationships of Generalized Hypergeometric Functions (GHFs) in one and two variables, delving into their unpredictable domain and their noteworthy correlations with K-Functions. GHFs are versatile numerical developments that are well-known for their flexible applications in many fields of research and design. In this paper, we characterize more generalized hypergeometric k-functions using an impressive example of Wright hypergeometric capacity. The basic representation, differential features, touching relations, and differential recipes of the generalized hypergeometric k-functions 2R1, k(a, b; c; τ; z) (k > 0) are somewhat outlined. The aim of this investigation study is to find the neigh boring capability relations for ????-hypergeometric functions with one boundary and, additionally, to obtain adjoining capacity relations for two boundaries, with reference to Gauss's fifteen bordering capability relations for hypergeometric functions. During this exploratory work, we find the touching capability relations for both cases up to the point where another boundary ????>0. In the case where ????→1, the touching capability relations for ????-hypergeometric functions are clearly Gauss coterminous capability relations.