Advances in applied mathematics vol:20 issue:2 pages:141-168
In this paper we compute the recurrence coefficients of orthogonal polynomials using T-function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potential which, for sufficiently large N is the second derivative of the free energy with respect to N, the particle number. We give three examples using this technique: Freud weights, Erods weights, and weak exponential weights. (C) 1998 Academic Press.