TY - JOUR
T1 - Zeros of polynomials orthogonal with respect to a signed weight
AU - Atia, M.J.
AU - Benabdallah, M.
AU - Costas-Santos, R.S.
JO - Indagationes Mathematicae
VL - 23
IS - 1
SP - 26
EP - 31
PY - 2012
DA - 2012/03/01/
SN - 0019-3577
DO - https://doi.org/10.1016/j.indag.2011.09.011
UR - https://www.sciencedirect.com/science/article/pii/S0019357711000590
KW - Zeros
KW - Real-rooted polynomials
KW - Generalized Jacobi polynomials
KW - Generalized Gegenbauer polynomials
AB - In this paper we consider the monic polynomial sequence (Pnα,q(x)) that is orthogonal on [−1,1] with respect to the weight function x2q+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