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Zeros of polynomials orthogonal with respect to a signed weight

In this paper we consider the polynomial sequence $(P_{n}^{α,q}(x))$ that is orthogonal on $[-1,1]$ with respect to the weight function $x^{2q+1}(1-x^{2})^α(1-x), α>-1, q\in \mathbb N$; we obtain the coefficients of the tree-term recurrence relation (TTRR) by using a different method from the one derived in \cite{kn:atia1}; we prove that the interlacing property does not hold properly for $(P_n^{α,q}(x))$; and we also prove that, if $x_{n,n}^{α+i,q+j}$ is the largest zero of $P_{n}^{α+i,q+j}(x)$, $\displaystyle x_{2n-2j,2n-2j}^{α+j,q+j}< x_{2n-2i,2n-2i}^{α+i,q+i}, 0\leq i<j\leq n-1$.