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 > ...
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
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, ...