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1: 30.11 Radial Spheroidal Wave Functions
§30.11 Radial Spheroidal Wave Functions
§30.11(i) Definitions
Connection Formulas
See accompanying text
Figure 30.11.4: S n 1 ( 1 ) ( i y , 2 i ) , n = 1 , 2 , 0 y 10 . Magnify
§30.11(v) Connection with the Ps and Qs Functions
2: 30.16 Methods of Computation
§30.16(iii) Radial Spheroidal Wave Functions
3: 30.17 Tables
§30.17 Tables
4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
30.14.8 w 1 ( ξ ) = a 1 S n m ( 1 ) ( i ξ , γ ) + b 1 S n m ( 2 ) ( i ξ , γ ) .
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
5: 30.1 Special Notation
The main functions treated in this chapter are the eigenvalues λ n m ( γ 2 ) and the spheroidal wave functions Ps n m ( x , γ 2 ) , Qs n m ( x , γ 2 ) , Ps n m ( z , γ 2 ) , Qs n m ( z , γ 2 ) , and S n m ( j ) ( z , γ ) , j = 1 , 2 , 3 , 4 . … Flammer (1957) and Abramowitz and Stegun (1964) use λ m n ( γ ) for λ n m ( γ 2 ) + γ 2 , R m n ( j ) ( γ , z ) for S n m ( j ) ( z , γ ) , and …
6: 30.13 Wave Equation in Prolate Spheroidal Coordinates
7: 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..
  • 8: Bibliography B
  • T. A. Beu and R. I. Câmpeanu (1983b) Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.
  • 9: Bibliography C
  • W. C. Connett, C. Markett, and A. L. Schwartz (1993) Product formulas and convolutions for angular and radial spheroidal wave functions. Trans. Amer. Math. Soc. 338 (2), pp. 695–710.
  • 10: Bibliography V
  • A. L. Van Buren, R. V. Baier, S. Hanish, and B. J. King (1972) Calculation of spheroidal wave functions. J. Acoust. Soc. Amer. 51, pp. 414–416.
  • 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 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.
  • Van Buren (website) Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation