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We show a method to construct isospectral deformations of classicalorthogonal polynomials. The construction is based on confluent Darbouxtransformations, and it allows to construct Sturm-Liouville problems withpolynomial eigenfunctions that have an arbitrary number of continuousparameters. We propose to call these new orthogonal polynomial systems\emph{exceptional polynomials of the second kind}. We illustrate thisconstruction by describing the class of exceptional Gegenbauer polynomials ofthe second kind.

Exceptional Gegenbauer polynomials via isospectral deformation