arXiv subjects

Kelly Postelmans

Publications and source records attributed to Kelly Postelmans.

2 recordsLinked to original sources

arXiv2006

Irrationality of $ζ_q(1)$ and $ζ_q(2)$

In this paper we show how one can obtain simultaneous rational approximants for $ζ_q(1)$ and $ζ_q(2)$ with a common denominator by means of Hermite-Pade approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, $ζ_q(1)$, $ζ_q(2)$ are linearly independent over the rationals. In particular this implies that $ζ_q(1)$ and $ζ_q(2)$ are irrational. Furthermore we give an upper bound for the measure of irrationality.

math.CA↗

arXiv2004

Multiple little q-Jacobi polynomials

We introduce two kinds of multiple little q-Jacobi polynomials by imposing orthogonality conditions with respect to r discrete little q-Jacobi measures on the exponential lattice q^k (k=0,1,2,3,...), where 0 < q < 1. We show that these multiple little q-Jacobi polynomials have useful q-difference properties, such as a Rodrigues formula (consisting of a product of r difference operators). Some properties of the zeros of these polynomials and some asymptotic properties will be given as well.

math.CA↗