Some $k$-Horn hypergeometric functions and their properties

Authors : Caner Çatak, Recep Şahin, Ali Olgun, Oğuz Yağci

Pages : 97-107

Doi:10.54187/jnrs.1335407

View : 61 | Download : 52

Publication Date : 2023-08-31

Article Type : Research Article

Abstract :In the theory of special functions, the $k$-Pochhammer symbol is a generalization of the Pochhammer symbol. With the help of the $k$-Pochhammer symbol, we introduce and study a new generalization of the $k$-Horn hypergeometric functions such as, ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$. Furthermore, several investigations have been carried out for some important recursion formulae for several one variable and two variables $k$-hypergeometric functions. In the light of these studies, we introduce some important recursion formulae for several newly generalized $k$-Horn hypergeometric functions. Finally, we present several relations between some $k$-Horn hypergeometric functions ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$, and $k$-Gauss hypergeometric functions $_{2}{F}_{1}^{k}$.
Keywords : $k$-Gamma function, $k$-Hypergeometric function, $k$-Gauss hypergeometric function, Recursion formula