A finite family of RI polynomials is introduced and studied. It consists in a set of polynomials of 3F2 form whose biorthogonality to an ensemble of rational functions is spelled out. These polynomials are shown to satisfy two generalized eigenvalue problems: in addition to their recurrence relation of RI type, they are also found to obey a difference equation. Underscoring this bispectrality is a triplet of operators with tridiagonal actions. The algebra associated to these operators is provided.
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Vinet et al. (2024) studied this question.
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