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Semi-commuting and commuting operators for the Heun family (1705.05795v1)
Published 16 May 2017 in math-ph, gr-qc, math.CA, and math.MP
Abstract: We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In particular, we discover that a certain generalized Heun equation commutes with the Heun differential operator allowing us to construct the general solution to a complicated fourth order linear differential equation with variable coefficients which Maple 16 cannot solve.
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