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A complete classification of Belyi functions for transforming certain hypergeometric equations to Heun equations is given. The considered hypergeometric equations have the local exponent differences 1/k, 1/ℓ, 1/m that satisfy k,ℓ,m∈N and the hyperbolic condition 1/k+1/ℓ+1/m<1. There are 366 Galois orbits of Belyi functions giving the considered (non-parametric) hypergeometric-to-Heun pull-back...
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