On the Markov sequence problem for Jacobi polynomials

Details On the Markov sequence problem for Jacobi polynomials On the Markov sequence problem for Jacobi polynomials

2008-05-07

arxiv.org/abs/0805.1046v2

Mathematics

Classical Analysis and ODEs

The second version contains additional material and references. In particular, we discuss a product formula of Koornwider and

Scientific paper

We give a simple and entirely elementary proof of Gasper's theorem on the Markov sequence problem for Jacobi polynomials. It is based on the spectral analysis of an operator that arises in the study of a probabilistic model of colliding molecules introduced by Marc Kac. In the process, we obtain some new integral formulas for ratios of Jacobi polynomials that generalize Gasper's product formula and a well known formula of Koornwinder.

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