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We introduce a nine-parameter Heun-type differential equation and obtainthree classes of its solutions as series of square integrable functions writtenin terms of the Jacobi polynomial. The expansion coefficients of the seriessatisfy three-term recursion relations, which are solved in terms of orthogonalpolynomials with continuous and/or discrete spectra. Some of these arewell-known polynomials while others are either new or modified versions ofknown ones.

Series solutions of Heun-type equation in terms of orthogonal polynomials