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Numerical aspects of Mathieu eigenvalues. (English) Zbl 0196.49901
References:
[1]Norman Bazley,Lower bounds for eigenvalues with application to the helium atom, Proc. Nat. Acad. Sci., 45, pp. 850–853, 1959. · Zbl 0087.43004 · doi:10.1073/pnas.45.6.850
[2]Norman Bazley,Lower bounds for eigenvalues, J. Math. Mech., Vol. 10, No. 2, pp. 289–307, 1961.
[3]G. Blanch,On the Computation of Mathieu Functions, J. Math. and Phys., Vol. XXV, No. 1, pp. 1–20, 1946.
[4]G. Blanch and I. Rhodes,Table of characteristic values of Mathieu’s equation for large values of the parameter, J. Washington Acad. Sci., Vol. 45, No. 6, pp. 166–196, 1955.
[5]G. Blanch,Numerical Evaluation of Continued Fractions, SIAM Rev., Vol. 6, No. 4, pp. 383–421, 1964. · Zbl 0133.38904 · doi:10.1137/1006092
[6]C. J. Bouwkamp,Theoretische en numericke Behandeling van de Buiging door een Ronde Opening, J. B. Wolters’ U.M., 1941. Diss. Groningen, Batavia.
[7]C. J. Bouwkamp,On Spheroidal Wave Functions of Order Zero, J. Math. Phys., 26, pp. 79–92, 1947.
[8]G. Fichera,Sul Calcolo degli Autovalori, Atti del simposio internazionale: Applicazione dell’Analisi alla Fisica Matematica, Cagliari-Lanasi, 1964.
[9]G. Fichera,Approximation and Estimates for Eigenvalues, Proc. of the Conference on Numerical Analysis, University of Maryland, May 1965.
[10]Fox and Stadter, Referenced in the Weinstein paper, [20].
[11]S. Goldstein,Mathieu Functions, Camb. Phil. Soc. Trans., Vol. 23, pp. 303–336, 1927.
[12]E. L. Ince,Tables of Elliptic Cylinder Functions, Roy. Soc. Edin. Proc., pp. 355–423, Vol. 52, 1932.
[13]N. W. McLachlan,Theory and Application of Mathieu Functions, Oxford, Clarendon Press, 1947.
[14]J. Meixner and F. W. Schäfke,Mathieusche Funktionen und Sphäroidfunktionen, Berlin, Springer, 1954.
[15]Françoise Michaud,Étude sur les représentations approchées des solutions de l’équation de Mathieu, Centre National de la Recherche Scientifique, Institut Blaise Pascal, Laboratoire de calcul numérique, Paris, June 1965.
[16]National Bureau of Standards,Tables Relating to Mathieu Functions, New York, Columbia University Press, 1951.
[17]Hanan Rubin,Anecdote on power series expansions of Mathieu functions, J. Math. and Phys., No. 4, pp. 339–341, 1964.
[18]A. Weinstein, Memorial Sc. Math. No. 88, 1937.
[19]A. Weinstein,Bounds for eigenvalues and the method of intermediate problems, Proceedings of the International Conference on Partial Differential Equations and Continuum Mechanics, Madison, Wis., pp. 39–53, University of Wisconsin Press, 1961.
[20]A. Weinstein,Some numerical results in intermediate problems for eigenvalues, Proc. of the Conference on Numerical Analysis, University of Maryland, May 1965.
[21]E. T. Whittaker and G. N. Watson,Modern Analysis, Cambridge, University Press, fourth edition (1927). reprinted in 1963.