On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients (Q1208855)

This interesting paper is devoted to the study of the generation of several sets of orthogonal polynomials that are useful in the solution of a number of physical problems. Recurrence relations involving the coefficients of the three-term recurrence relations of these polynomials are established and their numerical instability is then studied. Divergent asymptotic series for the recurrence coefficients are also obtained and these are subsequently used to establish accurate approximations.