The monotonicity properties of all the zeros with respect to a parameter of orthogonal polynomials
associated with an even weight function are studied. The results we obtain extend the
work of A. Markoff. The monotonicity of the zeros of Gegenbauer, Freud-type and symmetric
Meixner-Pollaczek orthogonal polynomials as well as Al-Salam-Chihara q-orthogonal polynomials
are investigated. For the Meixner-Pollaczek polynomials, a special case of a conjecture
by Jordaan and To´okos which concerns the interlacing of their zeros between two different
sequences of Meixner-Pollaczek polynomials is proved.
In this paper, we prove the quasi-orthogonality of a family of 2F2 polynomials and several classes of 3F2 polynomials that do not appear in the Askey scheme for hypergeometric orthogonal polynomials. Our results include, ...