Differentiation identities for hypergeometric functions
Classical Analysis and ODEs
2022-12-13 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2212.04271,
title = {Differentiation identities for hypergeometric functions},
author = {Hayato Motohashi},
journal= {arXiv preprint arXiv:2212.04271},
year = {2022}
}
Comments
14 pages, 1 figure