Determinant identities for moments of orthogonal polynomials

Abstract: We present a formula that expresses the Hankel determinants of a linear combination of length d+1 of moments of orthogonal polynomials in terms of a d x d determinant of the orthogonal polynomials. As a literature search revealed, this formula exists somehow hidden in the folklore of the theory of orthogonal polynomials as it is related to "Christoffel's theorem". In any case, it deserves to be better known and be presented correctly and with full proof. (During the talk I will explain the meaning of these somewhat cryptic formulations.) Subsequently, I will show an application of the formula. I will close the talk by presenting a generalisation that is inspired by Uvarov's formula for the orthogonal polynomials of rationally related densities.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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