On the Markov sequence problem for Jacobi polynomials
نویسندگان
چکیده
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. Mathematics Subject Classification Numbers: 31B10, 33C45, 37A40
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