An integral for the product of two Selberg-Jack symmetric polynomials
Kadell, Kevin W. J.
Compositio Mathematica, Tome 89 (1993), p. 5-43 / Harvested from Numdam
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Publié le : 1993-01-01
@article{CM_1993__87_1_5_0,
     author = {Kadell, Kevin W. J.},
     title = {An integral for the product of two Selberg-Jack symmetric polynomials},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {5-43},
     mrnumber = {1219451},
     zbl = {0788.33007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__87_1_5_0}
}

Kadell, Kevin W. J. An integral for the product of two Selberg-Jack symmetric polynomials. Compositio Mathematica, Tome 89 (1993) pp. 5-43. http://gdmltest.u-ga.fr/item/CM_1993__87_1_5_0/

[An2] G.E. Andrews: q-Series: Their Development and Applications in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, CBMS Regional Conference Series in Mathematics, number 66, American Mathematical Society, Providence, RI, 1986. | MR 858826 | Zbl 0594.33001

[Ao1] K. Aomoto: Jacobi polynomials associated with Selberg's integral, SIAM J. Math. Analysis 18 (1987), 545-549. | MR 876291 | Zbl 0639.33001

[Hab1] L. Habsieger: Une q-intégrale de Selberg-Askey, SIAM J. Math. Analysis 19 (1988), 1475-1489. | MR 965268 | Zbl 0664.33001

[Han1] P. Hanlon: Jack symmetric functions and some combinatorial properties of Young symmetrizers, J. Combinatorial Theory (A) 47 (1988), 37-80. | MR 924451 | Zbl 0641.20010

[Hu1] L.K. Hua: Harmonic analysis of functions of several complex variables in the complex domains. Translations of mathematical monographs, Vol. 6, Amer. Math. Soc., Providence, RI, 1963. | Zbl 0112.07402

[Ja1] H. Jack: A class of symmetric polynomials with a parameter, Proc. Royal Soc. Edinburgh (A)69 (1969-70), 1-17. | MR 289462 | Zbl 0198.04606

[Ka1] K.W.J. Kadell: A proof of some q-analogues of Selberg's integral for k = 1, SIAM J. Math. Analysis 19 (1988), 944-968. | MR 946654 | Zbl 0643.33003

[Ka2] K.W.J. Kadell: A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Analysis 19 (1988), 969-986. | MR 946655 | Zbl 0643.33004

[Ka3] K.W.J. Kadell: The q-Selberg polynomials for n = 2, Trans. Amer. Math. Soc. 310 (1988), 535-553. | MR 973170 | Zbl 0706.33015

[Ka4] K.W.J. Kadell: The Selberg-Jack symmetric functions, Advances in Math., to appear. | MR 1467311 | Zbl 0885.33009

[Ma1] I.G. Macdonald: Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 1979. | MR 553598 | Zbl 0487.20007

[Ma2] I.G. Macdonald: Second edition of [Ma1], to appear. | MR 1354144

[Ma3] I.G. Macdonald: Orthogonal polynomials associated with root systems, to appear. | MR 1100299 | MR 1817334 | Zbl 1032.33010

[Ri1] D. St. P. Richards: Analogs and Extensions of Selberg's integral, Proceedings of the IMA workshop on q-series and partitions, March 1988. | Zbl 0697.33007

[Se1] A. Selberg: Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 26 (1944), 71-78. | MR 18287 | Zbl 0063.06870

[St1] R.P. Stanley: Some combinatorial properties of Jack symmetric functions, Advances in Math. 77 (1989), 76-115. | MR 1014073 | Zbl 0743.05072

[Sz1] G. Szegö: Orthogonal Polynomials, Colloquium Publications, Vol. 23, American Mathematical Society, Providence, RI, 1975. | MR 372517 | Zbl 0305.42011 | Zbl 0023.21505

[Ze1] D. Zeilberger: A proof of the G2 case of Macdonald's root system-Dyson conjecture, SIAM J. Math. Analysis 18 (1987), 880-883. | MR 883574 | Zbl 0643.05004