9J-SYMBOLS OF THE OSCILLATOR ALGEBRA AND KRAWTCHOUK POLYNOMIALS IN 2 VARIABLES

Authors
Citation
A. Zhedanov, 9J-SYMBOLS OF THE OSCILLATOR ALGEBRA AND KRAWTCHOUK POLYNOMIALS IN 2 VARIABLES, Journal of physics. A, mathematical and general, 30(23), 1997, pp. 8337-8353
Citations number
31
Categorie Soggetti
Physics,"Physycs, Mathematical
ISSN journal
03054470
Volume
30
Issue
23
Year of publication
1997
Pages
8337 - 8353
Database
ISI
SICI code
0305-4470(1997)30:23<8337:9OTOAA>2.0.ZU;2-T
Abstract
A simple generating function for the 9j-symbols of the oscillator alge bra is found. On the basis of this function it is shown that correspon ding 9j-symbols are expressed in terms of polynomials Q(pr)(k, m) in t wo discrete variables which are orthogonal with respect to the trinomi al distribution. These polynomials depend on four independent paramete rs and can be considered as a two-dimensional analogue of the Krawtcho uk polynomials. Difference-difference relations, the factorization cha in, the duality property, and the Rodriguez formula for these polynomi als are obtained. It is shown that the polynomials Q(pr)(k, m) are eig enfunctions of two commuting difference operators. These polynomials a re also covariant with respect to two commuting difference derivation operators. In a special symmetric case these polynomials admit a simpl e factorized expression in terms of two distinct ordinary Krawtchouk p olynomials. In another special case we obtain an explicit expression o f 9j-symbols in terms of the Appell hypergeometric function F-1 in two variables.