E. Koelink

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math.CA2025

An evolution of matrix-valued orthogonal polynomials

Erik Koelink, Pablo RomÃ¡n, Wadim Zudilin

We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several…

math.CA2025

A partial-sum deformation for a family of orthogonal polynomials

Erik Koelink, Pablo RomÃ¡n, Wadim Zudilin

There are several questions one may ask about polynomials $q_{m} (x) = q_{m} (x; t) = \sum_{n = 0}^{m} t^{m} p_{n} (x)$ attached to a family of orthogonal polynomials ${p_{n} (x)}_{n \geq 0}$ . In this note…