Three-Term Relations for 3F2(1)

2016/04/02 by Ebisu, Akihito, Iwasaki, Katsunori
#33C20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00480

Abstract

For the hypergeometric function of unit argument 3F2(1) we prove the existence and uniqueness of three-term relations with arbitrary integer shifts. We show that not only the original 3F2(1) function but also other five functions related to it satisfy one and the same three-term relation. This fact is referred to as simultaneousness. The uniqueness and simultaneousness provide three-term relations with a group symmetry of order 72.

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