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$R_I$ biorthogonal polynomials of Hahn type (2209.07433v1)
Published 15 Sep 2022 in math.CA, math-ph, and math.MP
Abstract: A finite family of $R_I$ polynomials is introduced and studied. It consists in a set of polynomials of ${3}F{2}$ 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 $R_I$ type, they are also found to obey a difference equation. Underscoring this bispectrality is a triplet of operators with tridiagonal actions.
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