Journal ArticleDOI
The Hahn and Meixner polynomials of an imaginary argument and some of their applications
TLDR
In this article, the Hahn and Meixner polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter, leading to the origination of two systems of real polynomial systems orthogonal with respect to a continuous measure.Abstract:
The Hahn and Meixner polynomials belonging to the classical orthogonal polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter. This leads to the origination of two systems of real polynomials orthogonal with respect to a continuous measure. The Meixner polynomials of an imaginary argument obtained in this manner turned out to be known in the literature as the Pollaczek polynomials. The orthogonality relation for the Hahn polynomials with respect to a continuous measure is apparently new. A close connection between the Hahn polynomials of an imaginary argument and representations of the Lorentz group SO(3,1) is considered.read more
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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
Book ChapterDOI
Advanced determinant calculus
TL;DR: In this article, the reader is provided with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research.
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Advanced Determinant Calculus
TL;DR: In this paper, the reader is provided with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research.
Journal Article
On the moment problem
TL;DR: In this paper, the authors provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the theory of regularly varying functions.
Journal ArticleDOI
Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
H.T. Koelink,J. Van der Jeugt +1 more
TL;DR: In this article, the authors derived convolution identities for Al-Salam and Chihara polynomials by using the Clebsch-Gordan decomposition and the Racah coefficients.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Journal ArticleDOI
Quasi-optical approach in quantum field theory
TL;DR: In this paper, a quasi-optical approach to elementary particle scattering by quantum field theory concepts is derived, which makes possible construction of the generalized complex potential dependent on velocities.
Journal ArticleDOI
Quasipotential type equation for the relativistic scattering amplitude.
TL;DR: In this article, the quasipotential type equation for the relativistic scattering amplitude is obtained with the help of a special kind of perturbation theory, which is called perturbative perturbations.