@article{SIGMA_2018_14_a130,
author = {Hans Volkmer},
title = {Eigenvalue {Problems} for {Lam\'e's} {Differential} {Equation}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2018},
volume = {14},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a130/}
}
Hans Volkmer. Eigenvalue Problems for Lamé's Differential Equation. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a130/
[1] Arscott F. M., Periodic differential equations. An introduction to Mathieu, Lamé, and allied functions, International Series of Monographs in Pure and Applied Mathematics, 66, Pergamon Press, The Macmillan Co., New York, 1964
[2] Brack M., Mehta M., Tanaka K., “Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems”, J. Phys. A: Math. Gen., 34 (2001), 8199–8220, arXiv: nlin.CD/0105048 | DOI
[3] Eastham M. S. P., The spectral theory of periodic differential equations, Texts in Mathematics (Edinburgh), Scottish Academic Press, Edinburgh; Hafner Press, New York, 1973
[4] Erdélyi A., “On algebraic Lamé functions”, Philos. Mag., 32 (1941), 348–350
[5] Erdélyi A., “Lamé–Wangerin functions”, J. London Math. Soc., 23 (1948), 64–69 | DOI
[6] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher transcendental functions, v. III, McGraw-Hill Book Company, New York, 1955
[7] Finkel F., González-López A., Rodríguez M. A., “A new algebraization of the Lamé equation”, J. Phys. A: Math. Gen., 33 (2000), 1519–1542, arXiv: math-ph/9908002 | DOI
[8] Ince E. L., “Further investigations into the periodic Lamé functions”, Proc. Roy. Soc. Edinburgh, 60 (1940), 83–99
[9] Ince E. L., “The periodic Lamé functions”, Proc. Roy. Soc. Edinburgh, 60 (1940), 47–63
[10] Jansen J. K. M., Simple-periodic and non-periodic Lamé functions, Mathematical Centre Tracts, 72, Mathematisch Centrum, Amsterdam, 1977
[11] Kato T., Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995 | DOI
[12] Kong Q., Wu H., Zettl A., “Dependence of the $n$th Sturm–Liouville eigenvalue on the problem”, J. Differential Equations, 156 (1999), 328–354 | DOI
[13] Lambe C. G., “Lamé–Wangerin functions”, Quart. J. Math. Oxford Ser. 2, 3 (1952), 107–114 | DOI
[14] Magnus W., Winkler S., Hill's equation, Interscience Tracts in Pure and Applied Mathematics, 20, Interscience Publishers John Wiley Sons, New York–London–Sydney, 1966
[15] McCrea W. H., Newing R. A., “Boundary conditions for the wave equation”, Proc. London Math. Soc., 37 (1934), 520–534 | DOI
[16] Miller W. Jr., Symmetry and separation of variables, Encyclopedia of Mathematics and its Applications, 4, Addison-Wesley Publishing Co., Reading, Mass.–London–Amsterdam, 1977
[17] Moon P., Spencer D. E., Field theory handbook. Including coordinate systems, differential equations and their solution, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1961 | DOI
[18] Olver F. W.J., Lozier D. W., Boisvert R. F., Clark C. W. (eds), NIST handbook of mathematical functions, Cambridge University Press, Cambridge, 2010
[19] Perron O., “Über einen Satz des Herrn Poincaré”, J. Reine Angew. Math., 136 (1909), 17–38 | DOI
[20] Szegö G., Orthogonal polynomials, American Mathematical Society, Colloquium Publications, 23, 4th ed., Amer. Math. Soc., Providence, R.I., 1975
[21] Wangerin A., Reduction der Potentialgleichung für gewisse Rotationskörper auf eine gewöhnliche Differentialgleichung, S. Hirzel, Leipzig, 1875
[22] Whittaker E. T., Watson G. N., A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996 | DOI
[23] Zettl A., Sturm–Liouville theory, Mathematical Surveys and Monographs, 121, Amer. Math. Soc., Providence, RI, 2005