Root systems and hypergeometric functions. II

G. J. Heckman

Compositio Mathematica (1987)

  • Volume: 64, Issue: 3, page 353-373
  • ISSN: 0010-437X

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Heckman, G. J.. "Root systems and hypergeometric functions. II." Compositio Mathematica 64.3 (1987): 353-373. <http://eudml.org/doc/89880>.

@article{Heckman1987,
author = {Heckman, G. J.},
journal = {Compositio Mathematica},
keywords = {Nilsson class function; monodromy; hypergeometric function; Weyl group invariant analytic function; orthogonality relation; Jacobi polynomials; root system},
language = {eng},
number = {3},
pages = {353-373},
publisher = {Martinus Nijhoff Publishers},
title = {Root systems and hypergeometric functions. II},
url = {http://eudml.org/doc/89880},
volume = {64},
year = {1987},
}

TY - JOUR
AU - Heckman, G. J.
TI - Root systems and hypergeometric functions. II
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 64
IS - 3
SP - 353
EP - 373
LA - eng
KW - Nilsson class function; monodromy; hypergeometric function; Weyl group invariant analytic function; orthogonality relation; Jacobi polynomials; root system
UR - http://eudml.org/doc/89880
ER -

References

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  1. [D] P. Deligne, Équations Differentielles à Points Singuliers Réguliers, LNM 163, Springer Verlag (1970). Zbl0244.14004MR417174
  2. [HO] G.J. Heckman and E.M. Opdam, Root systems and hypergeometric functions I, Comp. Math.64 (1987) 329-352. Zbl0656.17006MR918416
  3. [Kl] F. Klein, Vorlesungen über die Hypergeometrische Funktion, Grundl. Math. Wissenschaften, Springer (1933). MR668700JFM59.0375.11
  4. [KO] M. Kashiwara and T. Oshima, Systems of differential equations with regular singularities and their boundary value problems, Ann of Math.106 (1977) 154-200. Zbl0358.35073MR482870
  5. [vdL] H. v.d. Lek, The homotopy type of complex hyperplane complements, Thesis, Nijmegen (1983). 
  6. [M] I.G. Macdonald, Some conjectures for root systems, Siam J. Math. Anal.13(6) (1982) 988-1007. Zbl0498.17006MR674768
  7. [Op] E.M. Opdam, Root systems and hypergeometric functions III, to appear in Comp. Math. Zbl0669.33007MR949270
  8. [Os] T. Oshima, A Definition of Boundary Values of Solutions of Partial Differential Equations with Regular Singularities, Publ. RIMS, Kyoto Univ19 (1983) 1203-1230. Zbl0559.35007MR723467
  9. [P] J. Plemelj, Problems in the Sense of Riemann and Klein, Interscience Publ. (1964). Zbl0124.28203MR174815
  10. [R] B. Riemann, Beiträge zur Theorie der durch die Gauss'sche Reihe F(α, β, y; x) darstellbaren Funktionen, Ges. Abh., 67-87 (1857). 
  11. [S] I.G. Sprinkhuizen-Kuyper, Orthogonal polynomials in 2 variables. A further analysis of the polynomials orthogonal over a region bounded by two lines and a parabola. Siam J. Math. Anal.7(4) (1976) 501-518. Zbl0332.33011MR415187
  12. [WW] E.T. Whittaker and G.T. Watson, A Course in Modern Analysis, Cambr. Univ. Press (1927). JFM45.0433.02

Citations in EuDML Documents

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  1. E. M. Opdam, Root systems and hypergeometric functions III
  2. E. M. Opdam, Root systems and hypergeometric functions IV
  3. Pavel Etingof, Konstantin Styrkas, Algebraic integrability of Schrodinger operators and representations of Lie algebras
  4. J. F. Van Diejen, Commuting difference operators with polynomial eigenfunctions
  5. G. C. M. Ruitenburg, Invariant ideals of polynomial algebras with multiplicity free group action
  6. I. G. MacDonald, Affine Hecke algebras and orthogonal polynomials
  7. E. M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group
  8. G. J. Heckman, Dunkl operators

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