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# An Explicit Polynomial Expression for a $q$-Analogue of the 9-$j$ Symbols

Published:2010-11-23
Printed: Feb 2011
• Mizan Rahman,
School of Mathematics and Statistics, Carleton University, Ottawa, ON
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## Abstract

Using standard transformation and summation formulas for basic hypergeometric series we obtain an explicit polynomial form of the $q$-analogue of the 9-$j$ symbols, introduced by the author in a recent publication. We also consider a limiting case in which the 9-$j$ symbol factors into two Hahn polynomials. The same factorization occurs in another limit case of the corresponding $q$-analogue.
 Keywords: 6-$j$ and 9-$j$ symbols, $q$-analogues, balanced and very-well-poised basic hypergeometric series, orthonormal polynomials in one and two variables, Racah and $q$-Racah polynomials and their extensions
 MSC Classifications: 33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D50 - Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable