P-symbols, Heun Identities, and 3F2 Identities

Details P-symbols, Heun Identities, and 3F2 Identities P-symbols, Heun Identities, and 3F2 Identities

2007-12-28

arxiv.org/abs/0712.4299v2

pp. 139-159 in `Special Functions and Orthogonal Polynomials' (eds. D. Dominici and R. S. Maier), American Mathematical Societ

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

The usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with four regular singular points. The identities discussed include ones coming from Moebius automorphisms and F-homotopies, and also quadratic and biquadratic transformations. The case when Hl is identical to a generalized hypergeometric function of 3F2 type is examined, and Pfaff and Euler transformations of 3F2(a1,a2,e+1;b1,e;x) are derived. They extend several 3F2 identities of Bailey and Slater.

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