论文标题
超几何$ {} _ 4f_3（1）$具有积分参数差异
Hypergeometric ${}_4F_3(1)$ with integral parameter differences
论文作者
论文摘要
在本文中，我们继续研究超几何函数$ {} _ 4f_3（1）$作为其七个参数的函数。在其他条件下，我们推断出该功能的几个还原公式，其中一个最高参数之一超过了底部参数之一，或者通过正整数或反向底部参数之一超过了一个最高参数，而超过了一个正面参数或两者。我们表明，所有此类案例都减少了单位参数差异的情况。后一种情况又可以用两个系列的某些线性组合来表示，涉及伽马功能的对数衍生物。
In this paper we continue investigation of the hypergeometric function ${}_4F_3(1)$ as the function of its seven parameters. We deduce several reduction formulas for this function under additional conditions that one of the top parameters exceeds one of the bottom parameters by a positive integer or reversely one of the bottom parameters exceeds one of the top parameters by a positive integer or both. We show that all such cases reduce to the case of the unit parameter difference. The latter case, in turn, can be expressed in terms of certain linear combination of two series involving the logarithmic derivative of the gamma function.
