New families of orthogonal polynomials

This paper provides with a generalization of the work by Wimp and Kiesel [Non-linear recurrence relations and some derived orthogonal polynomials, Ann. Numer. Math. 2 (1995) 169-180] who generated some new orthogonal polynomials from Chebyshev polynomials of second kind. We consider a class of polynomials P-n(x) defined by: P-n(x) = (a(n)x + b(n)) Pn-1(x) + (1 - a(n)) P-n (x), n = 0, 1, 2,..., a(0) not equal 1, where the P-k(x) are monic classical orthogonal polynomials satisfying the well-known three-term recurrence relation: Pn+1(x) = (x - beta(n))P-n(x) - gamma P-n(n-1)(x), n >= 1, P-1(x) = x - beta(0); P-0 (x) = 1. We explicitly derive the sequences a(n) and b(n) in general and illustrate by some concrete relevant examples. (c) 2005 Elsevier B.V. All rights reserved.