Weighted sums of orthogonal polynomials with positive zeros

[摘要] We study the two sequences of polynomials which arise as denominators of the approximants of even and odd order, respectively, of a Stieltjes fraction, and which may be defined alternatively as a sequence of orthogonal polynomials with positive zeros and the associated sequence of kernel polynomials. Motivated by problems in the setting of birth-death processes, where these sequences play a major role, we focus on the asymptotic behaviour of the sequences and establish convergence of certain weighted sums of the polynomials at hand.

[发布日期] 1995-12-29

[效力级别]  Proceedings Paper

[关键词] Stieltjes fraction;orthogonal polynomials;birth-death processes;weighted sums