论文标题
$ _ {p} f_ {p} $和$ _ {p+1} f_ {p} $具有任意参数的广义超几何函数及其kummer-和euler-type变换的添加公式
Addition formulas for the $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with arbitrary parameters and their Kummer- and Euler-type transformations
论文作者
论文摘要
我们获得了$ _ {p} f_ {p} $和$ _ {p+1} f_ {p} $具有通用参数的概括性超几何函数的添加公式。这些功能与这些函数的整体表示相结合来得出kummer-和euler-type变换，这些变换表达$ _ {p} f_ {p} f_ {p} \ left（x \ right）$ and $ _ {p+1} f_p \ weft（x \ weft（x \ weled）$ $ _ {p} f_ {p} \ left（-x \ right）$和$ _ {p+1} f_p \ left（-x \ right）$ functions。
We obtain addition formulas for $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with general parameters. These are utilized in conjunction with integral representations of these functions to derive Kummer- and Euler-type transformations that express $_{p}F_{p}\left(x\right)$ and $_{p+1}F_p\left(x\right)$ in the form of sums of $_{p}F_{p}\left(-x\right)$ and $_{p+1}F_p\left(-x\right)$ functions, respectively.
