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We introduce a ten-parameter ordinary linear differential equation of thesecond order with four singular points. Three of these are finite and regularwhereas the fourth is irregular at infinity. We use the tridiagonalrepresentation approach to obtain a solution of the equation as boundedinfinite series of square integrable functions that are written in terms of theJacobi polynomials. The expansion coefficients of the series satisfy three-termrecursion relation, which is solved in terms of a modified version of thecontinuous Hahn orthogonal polynomial.

Series solution of a ten-parameter second order differential equation with three regular and one irregular singularities