The Hahn and Meixner polynomials of an imaginary argument and some of their applications

N. M. Atakishiyev, S. K. Suslov

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

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.

Original languageEnglish (US)
Article number014
Pages (from-to)1583-1596
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume18
Issue number10
DOIs
StatePublished - Dec 1 1985
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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