5 papers · 1 filter
Spectral theory and special functions
Erik Koelink
A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applie…
Transmutation kernels for the little q-Jacobi function transform
Erik Koelink, Hjalmar Rosengren
The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel…
The Askey-Wilson function transform scheme
Erik Koelink, Jasper V. Stokman
In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only.…
The big q-Jacobi function transform
Erik Koelink, Jasper V. Stokman
We give a detailed description of the resolution of the identity of a second order -difference operator considered as an unbounded self-adjoint operator on two different Hilbert…
q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations
Nicola Ciccoli, Erik Koelink, Tom H. Koornwinder
The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's -summation we complemen…