AN APPLICATION OF A NEW THEOREM ON ORTHOGONAL POLYNOMIALS AND DIFFERENTIAL EQUATIONS

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Abstract
Recently this author proved that if an OPS satisfies a differential equation of the form then, under certain conditions, an orthogonalizing weight distribution can be found that simultaneously satisfies n distributional differential equations of orders 1,3,…2n-1. In this paper, we show how this theorem can be used to find a new sixth order equation having orthogonal polynomial eigenfunctions. The method seems more efficient than previous methods used by this author. We also discuss various properties of this OPS, including the appropriate boundary value problem.