n=0 be a sequence of orthogonal polynomials. We briefly review properties
of pn that have been used to derive upper and lower bounds for the largest and smallest zero
of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have
been obtained using different approaches are numerically compared and new bounds for extreme
zeros of q-Laguerre and little q-Jacobi polynomials are proved.
Using the q-version of Zeilberger's algorithm, we provide a procedure to find mixed recurrence equations satisfied by classical q-orthogonal polynomials with shifted parameters. These equations are used to investigate ...
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
Driver, K.; Jooste, Alta(Taylor and Francis, 2017-04)
We consider the interlacing of zeros of polynomials within the sequences of quasi-orthogonal order one Meixner polynomials characterised by −β, c ∈ (0, 1). The interlacing of zeros of quasi-orthogonal Meixner polynomials ...