Identities between Appell's and hypergeometric functions

Details Identities between Appell's and hypergeometric functions Identities between Appell's and hypergeometric functions

2008-04-04

arxiv.org/abs/0804.0655v2

J. Math. Anal. Appl., Vol. 355 (2009), pg. 145-163

Mathematics

Classical Analysis and ODEs

30 pages; A few wrong evaluations of the published version are rectified (see arXiv:0906.1861)

Scientific paper

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.

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