A general mixed recurrence identifies a quadratic whose zeros complete interlacing for pairs of orthogonal polynomials failing by exactly two points, with explicit locations and applications to Jacobi, Meixner-Pollaczek, and Pseudo-Jacobi families.
Finite sequences of orthogonal polynomials connected by a Jacobi matrix
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Interlacing of zeros of polynomials completed with two additional points
A general mixed recurrence identifies a quadratic whose zeros complete interlacing for pairs of orthogonal polynomials failing by exactly two points, with explicit locations and applications to Jacobi, Meixner-Pollaczek, and Pseudo-Jacobi families.