Differentiation identities for hypergeometric functions
Differentiation identities for hypergeometric functions
复制标题
超几何函数的微分恒等式
DOI：
10.1016/j.exmath.2022.07.005
复制
发表时间：
2022
影响因子：
0.7
通讯作者：
Motohashi Hayato
中科院分区：
文献类型：
--
作者：
Motohashi Hayato;Suyama Teruaki;Motohashi Hayato
众所周知，超几何函数乘以某个幂函数的微分会产生另一个具有不同参数集的超几何函数。超几何函数的这种微分恒等式已广泛应用于应用数学和自然科学的各个领域。在本说明性注释中，我们提供了微分恒等式的简单证明，该证明仅基于超几何函数的幂级数展开的系数的定义。
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences. In this expository note, we provide a simple proof of the differentiation identities, which is based only on the definition of the coefficients for the power series expansion of the hypergeometric functions.