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1: Bibliography X
  • H. Xiao, V. Rokhlin, and N. Yarvin (2001) Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.
  • 2: 30.13 Wave Equation in Prolate Spheroidal Coordinates
    §30.13(i) Prolate Spheroidal Coordinates
    §30.13(ii) Metric Coefficients
    §30.13(iii) Laplacian
    §30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
    3: Bibliography V
  • A. L. Van Buren, B. J. King, R. V. Baier, and S. Hanish (1975) Tables of Angular Spheroidal Wave Functions, Vol. 1, Prolate, m = 0 ; Vol. 2, Oblate, m=0. Naval Res. Lab. Reports, Washington, D.C..
  • A. L. Van Buren and J. E. Boisvert (2002) Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives. Quart. Appl. Math. 60 (3), pp. 589–599.
  • A. L. Van Buren and J. E. Boisvert (2004) Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives. Quart. Appl. Math. 62 (3), pp. 493–507.
  • 4: 30.9 Asymptotic Approximations and Expansions
    §30.9(i) Prolate Spheroidal Wave Functions
    5: 30.2 Differential Equations
    In applications involving prolate spheroidal coordinates γ 2 is positive, in applications involving oblate spheroidal coordinates γ 2 is negative; see §§30.13, 30.14. …
    6: 30.4 Functions of the First Kind
    When γ 2 > 0 Ps n m ( x , γ 2 ) is the prolate angular spheroidal wave function, and when γ 2 < 0 Ps n m ( x , γ 2 ) is the oblate angular spheroidal wave function. If γ = 0 , Ps n m ( x , 0 ) reduces to the Ferrers function P n m ( x ) : …
    7: 30.1 Special Notation
    8: 14.30 Spherical and Spheroidal Harmonics
    P n m ( x ) and Q n m ( x ) ( x > 1 ) are often referred to as the prolate spheroidal harmonics of the first and second kinds, respectively. …
    9: Bibliography K
  • B. J. King, R. V. Baier, and S. Hanish (1970) A Fortran computer program for calculating the prolate spheroidal radial functions of the first and second kind and their first derivatives. NRL Report No. 7012 Naval Res. Lab.  Washingtion, D.C..
  • B. J. King and A. L. Van Buren (1970) A Fortran computer program for calculating the prolate and oblate angle functions of the first kind and their first and second derivatives. NRL Report No. 7161 Naval Res. Lab.  Washingtion, D.C..
  • 10: Bibliography S
  • D. Slepian and H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.
  • D. Slepian (1964) Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions. Bell System Tech. J. 43, pp. 3009–3057.