A Generalization of Selberg ' S Beta Integral

@inproceedings{Gustafson2007AGO,
  title={A Generalization of Selberg ' S Beta Integral},
  author={Robert A. Gustafson},
  year={2007}
}
We evaluate several infinite families of multidimensional integrals which are generalizations or analogs of Euler's classical beta integral. We first evaluate a ^-analog of Selberg's beta integral. This integral is then used to prove the Macdonald-Morris conjectures for the affine root systems of types S{Ci) and S{Cj) and to give a new proof of these conjectures for SiBC;), S{B(), 5 (B/) V and S*(£/) • 

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References

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Showing 1-10 of 17 references

A proof of the G2 case of Macdonald's root system-Dyson conjecture

  • D. Zeilberger
  • SIAM J. Math. Anal
  • 1987
Highly Influential
6 Excerpts

Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials

  • R. Askey, J. Wilson
  • Mem. Amer. Math. Soc, no
  • 1985
Highly Influential
9 Excerpts

Constant term identities for finite and affine root systems: conjectures and theorems

  • W. G. Morris
  • Ph. D. thesis, Univ. of Wisconsin-Madison,
  • 1982
Highly Influential
4 Excerpts

Some hypergeometric orthogonal polynomials

  • J. A. Wilson
  • SIAM J. Math. Anal
  • 1980
Highly Influential
7 Excerpts

Proof of a conjecture of Dyson

  • K. Wilson
  • J. Math. Phys
  • 1962
Highly Influential
7 Excerpts

Another conjectured q-Selberg integral

  • M. Rahman
  • SIAM J. Math. Anal
  • 1986
Highly Influential
3 Excerpts

Problems and prospects for basic hypergeometric functions, The Theory and Applications of Special Functions, (R. Askey, éd.)

  • G. Andrews
  • 1975
Highly Influential
4 Excerpts

Statistical theory of the energy levels of complex systems

  • F. J. Dyson
  • I, J. Math. Phys
  • 1962
Highly Influential
8 Excerpts

Jacobi polynomials associated with Selberg integrals

  • K. Aomoto
  • SIAM J. Math. Anal
  • 1987
3 Excerpts

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