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.
We investigate the zeros of a family of hypergeometric polynomials Mn (x; β, c) = (β)n 2F1 (-n, -x; β; 1 – 1/c), n ϵ N, known as Meixner polynomials, that are orthogonal on (0,∞) with respect to a discrete measure for β > ...
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, ...
The family of general Jacobi polynomials P(α,β)
n where α, β ∈ C can be characterised by complex (non-
Hermitian) orthogonality relations (cf. Kuijlaars et al. (2005)). The special subclass of Jacobi polynomials