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Explicit representations of biorthogonal polynomials

Arieh Iserles·Syvert Paul Nørsett
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Abstract

Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orthogonal polynomials.

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Arieh Iserles, Syvert Paul Nørsett. 1994-04-22. Explicit representations of biorthogonal polynomials. https://doi.org/10.1007/bf02198296

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