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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $ q$-Selberg polynomials for $ n=2$


Author: Kevin W. J. Kadell
Journal: Trans. Amer. Math. Soc. 310 (1988), 535-553
MSC: Primary 05A30; Secondary 33A15, 33A30, 33A75
MathSciNet review: 973170
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Abstract: We have conjectured that Selberg's integral has a plethora of extensions involving the Selberg polynomials and proved that these are the Schur functions for $ k = 1$. We prove this conjecture for $ n = 2$ and show that the polynomials are, in a formal sense, Jacobi polynomials. We conjecture an orthogonality relation for the Selberg polynomials which combines orthogonality relations for the Schur functions and Jacobi polynomials. We extend a basic Schur function identity.

We give a $ q$-analogue of the Selberg polynomials for $ n = 2$ using the little $ q$-Jacobi polynomials.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0973170-3
PII: S 0002-9947(1988)0973170-3
Article copyright: © Copyright 1988 American Mathematical Society