Sharp estimates for Jacobi matrices and chain sequences, II

[摘要] Chain sequences are positive sequences{c(n)} of the form c(n) = g(n)(1 - g(n-1)) for a nonnegative sequence {g(n)}. They are very useful in estimating the norms of Jacobi matrices and for localizing the interval of orthogonality for orthogonal polynomials. We give optimal estimates for the chain sequences which are more precise than the ones obtained in the paper (Constructive Approx. 6 (1990) 363) and in our earlier paper (J. Approx. Theory 118 (2002) 94). (C) 2003 Published by Elsevier Inc.

[发布日期] 2003-12-01

[关键词] orthogonal polynomials;chain sequences;Jacobi matrices;recurrence relation