Explicit representations of biorthogonal polynomials

Details Explicit representations of biorthogonal polynomials Explicit representations of biorthogonal polynomials

1994-04-22

arxiv.org/abs/math/9404224v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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