We prove results for the interlacing of zeros of Jacobi polynomials of the same or adjacent degree as one or both of the parameters are shifted continuously within a certain range. Numerical examplesâ€¦ (More)

We show that the zeros of the hypergeometric polynomials $$F\left( { - n,kn + 1;kn + 2;z} \right)$$ , $$k,n \in \mathbb{N}$$ , cluster on the loop of the lemniscate $$\left\{ {z:|z^k \left( {1 - z}â€¦ (More)

Stieltjesâ€™ Theorem (cf. [11]) proves that if {pn}n=0 is an orthogonal sequence, then between any two consecutive zeros of pk there is at least one zero of pn for all positive integers k, k < n; aâ€¦ (More)

We investigate the interlacing of the zeros of linear combinations pn + aqm with the zeros of the components pn and qm, where {pn} âˆž n=0 and {qm} âˆž m=0 are different sequences of Jacobi polynomials.â€¦ (More)

We use mixed three term recurrence relations typically satisfied by classical orthogonal polynomials from sequences corresponding to different parameters to derive upper (lower) bounds for theâ€¦ (More)