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zonal polynomials

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11: Bibliography T
  • A. Takemura (1984) Zonal Polynomials. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 4, Institute of Mathematical Statistics, Hayward, CA.
  • 12: Bibliography Z
  • Zeilberger (website) Doron Zeilberger’s Maple Packages and Programs Department of Mathematics, Rutgers University, New Jersey.
  • 13: Bibliography P
  • A. M. Parkhurst and A. T. James (1974) Zonal Polynomials of Order 1 Through 12 . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.
  • 14: 18.38 Mathematical Applications
    Zonal Spherical Harmonics
    Ultraspherical polynomials are zonal spherical harmonics. …
    15: Bibliography G
  • K. I. Gross and D. St. P. Richards (1987) Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
  • 16: Bibliography L
  • L. Lapointe and L. Vinet (1996) Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178 (2), pp. 425–452.
  • 17: Bibliography K
  • T. H. Koornwinder (1993) Askey-Wilson polynomials as zonal spherical functions on the SU ( 2 ) quantum group. SIAM J. Math. Anal. 24 (3), pp. 795–813.
  • 18: Bibliography S
  • J. R. Stembridge (1995) A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.
  • Stembridge (website) John Stembridge’s Home Page
  • 19: 14.18 Sums
    For expansions of arbitrary functions in series of Legendre polynomials see §18.18(i), and for expansions of arbitrary functions in series of associated Legendre functions see Schäfke (1961b). …
    Zonal Harmonic Series
    For a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22). …