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1: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14(i) Oblate Spheroidal Coordinates
§30.14(ii) Metric Coefficients
§30.14(iii) Laplacian
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
2: Bibliography V
  • A. L. Van Buren, R. V. Baier, and S. Hanish (1970) A Fortran computer program for calculating the oblate spheroidal radial functions of the first and second kind and their first derivatives. NRL Report No. 6959 Naval Res. Lab.  Washingtion, D.C..
  • 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..
  • 3: 30.9 Asymptotic Approximations and Expansions
    §30.9(ii) Oblate Spheroidal Wave Functions
    4: 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. …
    5: 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 ) : …
    6: 14.30 Spherical and Spheroidal Harmonics
    P n m ( i x ) and Q n m ( i x ) ( x > 0 ) are known as oblate spheroidal harmonics of the first and second kinds, respectively. Segura and Gil (1999) introduced the scaled oblate spheroidal harmonics R n m ( x ) = e - i π n / 2 P n m ( i x ) and T n m ( x ) = i e i π n / 2 Q n m ( i x ) which are real when x > 0 and n = 0 , 1 , 2 , . …
    7: 30.1 Special Notation
    8: Bibliography J
  • S. Jorna and C. Springer (1971) Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions p s ¯ n r ( η , h ) and q s ¯ n r ( η , h ) for large h . Proc. Roy. Soc. London Ser. A 321, pp. 545–555.
  • 9: Bibliography D
  • T. M. Dunster (1992) Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter λ . Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
  • T. M. Dunster (1995) Uniform asymptotic expansions for oblate spheroidal functions II: Negative separation parameter λ . Proc. Roy. Soc. Edinburgh Sect. A 125 (4), pp. 719–737.
  • 10: Bibliography H
  • S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King (1970) Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, m = 0 , 1 , 2 ; Vols. 4-6, Oblate, m = 0 , 1 , 2 . Technical report Naval Research Laboratory, Washington, D.C..