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.
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
Nangho, Maurice Kenfack; Jordaan, Kerstin(National Academy of Science of Ukraine, 2018-11-27)
We prove an equivalence between the existence of the rst structure relation
satis ed by a sequence of monic orthogonal polynomials fPng1n
=0, the orthogonality of the
second derivatives fD2
=2 and a generalized ...