Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4643142 | Journal of Computational and Applied Mathematics | 2006 | 10 Pages |
Abstract
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)=(anx+bn)Pn-1(x)+(1-an)Pn(x),n=0,1,2,…,a0≠1, where the Pk(x)Pk(x) are monic classical orthogonal polynomials satisfying the well-known three-term recurrence relation: Pn+1(x)=(x-βn)Pn(x)-γnPn-1(x),n⩾1,P1(x)=x-β0;P0(x)=1. We explicitly derive the sequences anan and bnbn in general and illustrate by some concrete relevant examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
C. Hounga, M.N. Hounkonnou, A. Ronveaux,