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1: 29.11 Lamé Wave Equation
§29.11 Lamé Wave Equation
The Lamé (or ellipsoidal) wave equation is given by …
2: 29.18 Mathematical Applications
The wave equation (29.18.1), when transformed to ellipsoidal coordinates α , β , γ : …
3: Bibliography
  • F. M. Arscott (1956) Perturbation solutions of the ellipsoidal wave equation. Quart. J. Math. Oxford Ser. (2) 7, pp. 161–174.
  • F. M. Arscott (1959) A new treatment of the ellipsoidal wave equation. Proc. London Math. Soc. (3) 9, pp. 21–50.
  • 4: Bibliography S
  • B. D. Sleeman (1968a) Integral equations and relations for Lamé functions and ellipsoidal wave functions. Proc. Cambridge Philos. Soc. 64, pp. 113–126.
  • 5: 30.13 Wave Equation in Prolate Spheroidal Coordinates
    §30.13 Wave Equation in Prolate Spheroidal Coordinates
    The wave equation
    §30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
    Equation (30.13.7) for ξ ξ 0 , and subject to the boundary condition w = 0 on the ellipsoid given by ξ = ξ 0 , poses an eigenvalue problem with κ 2 as spectral parameter. …
    6: 30.14 Wave Equation in Oblate Spheroidal Coordinates
    §30.14 Wave Equation in Oblate Spheroidal Coordinates
    §30.14(i) Oblate Spheroidal Coordinates
    §30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
    Equation (30.13.7) for ξ ξ 0 together with the boundary condition w = 0 on the ellipsoid given by ξ = ξ 0 , poses an eigenvalue problem with κ 2 as spectral parameter. …
    7: Bibliography M
  • J. Meixner (1944) Die Laméschen Wellenfunktionen des Drehellipsoids. Forschungsbericht No. 1952 ZWB (German).
  • J. W. Miles (1975) Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.
  • H. J. W. Müller (1966a) Asymptotic expansions of ellipsoidal wave functions and their characteristic numbers. Math. Nachr. 31, pp. 89–101.
  • H. J. W. Müller (1966b) Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions. Math. Nachr. 32, pp. 49–62.
  • H. J. W. Müller (1966c) On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.
  • 8: Bibliography H
  • J. Hammack, D. McCallister, N. Scheffner, and H. Segur (1995) Two-dimensional periodic waves in shallow water. II. Asymmetric waves. J. Fluid Mech. 285, pp. 95–122.
  • F. E. Harris (2002) Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Internat. J. Quantum Chem. 88 (6), pp. 701–734.
  • E. W. Hobson (1931) The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.
  • L. E. Hoisington and G. Breit (1938) Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.
  • C. Hunter and B. Guerrieri (1982) The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.
  • 9: Bibliography W
  • G. N. Watson (1935b) The surface of an ellipsoid. Quart. J. Math., Oxford Ser. 6, pp. 280–287.
  • J. V. Wehausen and E. V. Laitone (1960) Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.
  • J. A. Wheeler (1937) Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.
  • G. B. Whitham (1974) Linear and Nonlinear Waves. John Wiley & Sons, New York.
  • R. L. Wiegel (1960) A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.
  • 10: Bibliography C
  • B. C. Carlson (1961a) Ellipsoidal distributions of charge or mass. J. Mathematical Phys. 2, pp. 441–450.
  • T. W. Chaundy (1969) Elementary Differential Equations. Clarendon Press, Oxford.
  • 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.
  • D. C. Cronemeyer (1991) Demagnetization factors for general ellipsoids. J. Appl. Phys. 70 (6), pp. 2911–2914.
  • A. R. Curtis (1964a) Coulomb Wave Functions. Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.