Sharp estimates for Jacobi matrices and chain sequences, II Original Research Article

Chain sequences are positive sequences {cn} of the form cn=gn(1−gn−1) for a nonnegative sequence {gn}. 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).