The $q$-Selberg polynomials for $n=2$
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- by Kevin W. J. Kadell PDF
- Trans. Amer. Math. Soc. 310 (1988), 535-553 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 535-553
- MSC: Primary 05A30; Secondary 33A15, 33A30, 33A75
- DOI: https://doi.org/10.1090/S0002-9947-1988-0973170-3
- MathSciNet review: 973170