Identities between Appell's and hypergeometric functions
Classical Analysis and ODEs
2013-10-04 v2
Abstract
Univariate specializations of Appell's hypergeometric functions F1, F2, F3, F4 satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2, and could be simple (pullback) transformations of Euler's differential equation for the Gauss hypergeometric function. The paper classifies these cases, and presents corresponding relations between univariate specializations of Appell's functions and univariate hypergeometric functions. The computational aspect and interesting identities are discussed.
Cite
@article{arxiv.0804.0655,
title = {Identities between Appell's and hypergeometric functions},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:0804.0655},
year = {2013}
}
Comments
30 pages; A few wrong evaluations of the published version are rectified (see arXiv:0906.1861)