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Lamé wave equation


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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
§29.18(i) Sphero-Conal Coordinates
where u 1 , u 2 , u 3 each satisfy the Lamé wave equation (29.11.1). …
3: Bibliography F
  • M. V. Fedoryuk (1989) The Lamé wave equation. Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).
  • 4: 31.18 Methods of Computation
    The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 2830.
    5: 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.
  • 6: Hans Volkmer
    Volkmer has published numerous papers on special functions, spectral theory, differential equations, and mathematical statistics. …
  • 7: 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.
  • G. Vedeler (1950) A Mathieu equation for ships rolling among waves. I, II. Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.
  • H. Volkmer (1982) Integral relations for Lamé functions. SIAM J. Math. Anal. 13 (6), pp. 978–987.
  • H. Volkmer (2004a) Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.
  • H. Volkmer (2004b) Four remarks on eigenvalues of Lamé’s equation. Anal. Appl. (Singap.) 2 (2), pp. 161–175.
  • 8: 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.
  • F. M. Arscott (1964a) Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.
  • F. M. Arscott (1964b) Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions. International Series of Monographs in Pure and Applied Mathematics, Vol. 66, Pergamon Press, The Macmillan Co., New York.
  • F. M. Arscott (1967) The Whittaker-Hill equation and the wave equation in paraboloidal co-ordinates. Proc. Roy. Soc. Edinburgh Sect. A 67, pp. 265–276.
  • 9: Bibliography I
  • Y. Ikebe (1975) The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.
  • E. L. Ince (1926) Ordinary Differential Equations. Longmans, Green and Co., London.
  • E. L. Ince (1940a) The periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
  • E. L. Ince (1940b) Further investigations into the periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
  • A. Iserles (1996) A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.
  • 10: Bibliography R
  • H. A. Ragheb, L. Shafai, and M. Hamid (1991) Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.
  • S. O. Rice (1954) Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.
  • S. Ritter (1998) On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.
  • G. M. Roper (1951) Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations. Technical Reports and Memoranda Technical Report 2865, Aeronautical Research Council (Great Britain).
  • J. Rushchitsky and S. Rushchitska (2000) On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.