The symmetries of the 2phi1

Details The symmetries of the 2phi1 The symmetries of the 2phi1

2008-07-02

arxiv.org/abs/0807.0313v1

Mathematics

Combinatorics

14 pages

Scientific paper

We show that the only symmetries of the 2phi1 within a large class of possible transformations are Heine's transformations. The class of transformations considered consists of equation of the form 2phi1(a,b;c;q,z)= f(a,b,c,z) 2phi1(L(a,b,c,q,z)), where f is a q-hypergeometric term and L a linear operator on the logarithms of the parameters. We moreover prove some results on q-difference equations satisfied by 2phi1, which are used to prove the main result.

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