On the support of the measure of orthogonality of a class of orthogonal polynomials

摘要

For orthogonal polynomials of the formpnQn+1(x)+qnQn−1(x)+rnQn(x)=xQn(x),Q0(x)=0,Q1(x)=1,where pn>0,qn>0,rn∈R and limn→∞pn=limn→∞qn=1/2, a general sufficient condition is found such that the support of the measure of orthogonality is the entire interval [−1,1]. Starting from this result, more general cases of orthogonal polynomials are studied as a perturbation problem. The results are applied to Pollaczek polynomials, Random-walk polynomials (RWP), Neutron-transport polynomials and generalized co-recursive polynomials.