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5 papers
On q-analogues of the Fourier and Hankel transforms
Tom H. Koornwinder, René F. Swarttouw
For the third q-Bessel function (first introduced by F.H. Jackson, later rediscovered by W.Hahn in a special case and by H. Exton) we derive Hansen-Lommel type orthogonality relati…
Orthogonal Polynomials
Vilmos Totik
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discusse…
On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials
Erik Koelink, René F. Swarttouw
For the Bessel function \begin{equation} \label{bessel} J_ν(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{ν+2k}}{k! Γ(ν+1+k)} \end{equation} there exist…
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek, René F. Swarttouw
We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and…
A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel function
Erik Koelink, René F. Swarttouw
An addition and product formula for the Hahn-Exton -Bessel function, previously obtained by use of a quantum group theoretic interpretation, are proved analytically. A (formal)…