Differentiation identities for hypergeometric functions
arXiv:2212.04271 · doi:10.1016/j.exmath.2022.07.005
Abstract
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.
14 pages, 1 figure