TY  - JOUR
T1  - Some $k$-Horn hypergeometric functions and their properties
AU  - Yağcı, Oğuz
AU  - Çatak, Caner
AU  - Şahin, Recep
AU  - Olgun, Ali
PY  - 2023
DA  - August
DO  - 10.54187/jnrs.1335407
JF  - Journal of New Results in Science
JO  - JNRS
PB  - Tokat Gaziosmanpasa University
WT  - DergiPark
SN  - 1304-7981
SP  - 97
EP  - 107
VL  - 12
IS  - 2
LA  - en
AB  - 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 $_{2}{F}_{1}^{k}$.
KW  - $k$-Gamma function
KW  - $k$-Hypergeometric function
KW  - $k$-Gauss hypergeometric function
KW  - Recursion formula
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UR  - https://doi.org/10.54187/jnrs.1335407
L1  - https://dergipark.org.tr/en/download/article-file/3298384
ER  -