Christian.Krattenthaler

Affiliation: Universität Wien

Title Of Talk: Uvarov's formula --- a thorough discussion

Abstract: Christoffel's classical theorem provides a determinantal formula for the orthogonal polynomials corresponding to a polynomial deformation of a given measure in terms of the original orthogonal polynomials. Uvarov's formula from around 1960 provides a generalisation to the case of a rational deformation of a given measure. While the formula has been widely used since then, it seems that it has never been rigorously proved. After reviewing some history, I shall present a determinant identity that implies Uvarov's formula. To the best of my knowledge, this constitutes the first rigorous proof of the formula.

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