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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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