Zeros of polynomials orthogonal with respect to a signed weight

In this paper we consider the monic polynomial sequence (Pnα,q(x)) that is orthogonal on [−1,1][−1,1] with respect to the weight function x2q+1(1−x2)α(1−x),α>−1,q∈Nx2q+1(1−x2)α(1−x),α>−1,q∈N; we obtain the coefficients of the tree-term recurrence relation(TTRR) by using a different method from the one derived in Atia et al. (2002) [2]; we prove that the interlacing property does not hold properly for (Pnα,q(x)); and we also prove that, if xn,nα+i,q+j is the largest zero of Pnα+i,q+j(x), x2n−2j,2n−2jα+j,q+j