论文标题
在某些$ k $ - APPELL功能的解析和通过$ K $ -Trestional dermational derivative产生关系的公式
On some formulas for the $k$-analogue of Appell functions and generating relations via $k$-fractional derivative
论文作者
论文摘要
我们目前的研究主要基于$ k $ - hypheremetric函数，这些函数是通过使用pochhammer $ k $ -symbol \ cite {diaz}来构建的，这是超几何函数的重要概括之一。我们介绍了$ f_ {2} \ $和$ f_ {3} $ appell函数$ f_ {2} \ $的$ k $ -Analogues，分别由符号$ f_ {2，k} \ $和$ f_ {3，k} \ $的符号函数，就像Mubeen等人一样。在2015年\ cite {mubeen6}为$ f_ {1} $做。同时，我们证明了一些主要属性，即积分表示，转换公式和一些还原公式，这些公式不仅有助于我们在$ k $ -appell函数之间建立关系，还可以帮助我们之间的关系。最后，采用Riemann liouville $ k $ - 分类衍生物\ cite {rahman}并使用我们在本文中考虑的关系，我们获得了线性和双线性生成关系，以$ k $ $ k $ - $ k $ analogue的超角度功能和appell功能。
Our present investigation is mainly based on the $k$-hypergeometric functions which are constructed by making use of the Pochhammer $k$-symbol \cite{Diaz} which are one of the vital generalization of hypergeometric functions. We introduce $k$-analogues of $F_{2}\ $and $F_{3}$ Appell functions denoted by the symbols $F_{2,k}\ $and $F_{3,k}\ $respectively, just like Mubeen et al. did for $F_{1}$ in 2015 \cite{Mubeen6}. Meanwhile, we prove some main properties namely integral representations, transformation formulas and some reduction formulas which help us to have relations between not only $k$-Appell functions but also $k$-hypergeometric functions. Finally, employing the theory of Riemann Liouville $k$-fractional derivative \cite{Rahman} and using the relations which we consider in this paper, we acquire linear and bilinear generating relations for $k$-analogue of hypergeometric functions and Appell functions.
