References
Norman Bazley,Lower bounds for eigenvalues with application to the helium atom, Proc. Nat. Acad. Sci., 45, pp. 850–853, 1959.
Norman Bazley,Lower bounds for eigenvalues, J. Math. Mech., Vol. 10, No. 2, pp. 289–307, 1961.
G. Blanch,On the Computation of Mathieu Functions, J. Math. and Phys., Vol. XXV, No. 1, pp. 1–20, 1946.
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.
G. Blanch,Numerical Evaluation of Continued Fractions, SIAM Rev., Vol. 6, No. 4, pp. 383–421, 1964.
C. J. Bouwkamp,Theoretische en numericke Behandeling van de Buiging door een Ronde Opening, J. B. Wolters' U.M., 1941. Diss. Groningen, Batavia.
C. J. Bouwkamp,On Spheroidal Wave Functions of Order Zero, J. Math. Phys., 26, pp. 79–92, 1947.
G. Fichera,Sul Calcolo degli Autovalori, Atti del simposio internazionale: Applicazione dell'Analisi alla Fisica Matematica, Cagliari-Lanasi, 1964.
G. Fichera,Approximation and Estimates for Eigenvalues, Proc. of the Conference on Numerical Analysis, University of Maryland, May 1965.
Fox and Stadter, Referenced in the Weinstein paper, [20].
S. Goldstein,Mathieu Functions, Camb. Phil. Soc. Trans., Vol. 23, pp. 303–336, 1927.
E. L. Ince,Tables of Elliptic Cylinder Functions, Roy. Soc. Edin. Proc., pp. 355–423, Vol. 52, 1932.
N. W. McLachlan,Theory and Application of Mathieu Functions, Oxford, Clarendon Press, 1947.
J. Meixner and F. W. Schäfke,Mathieusche Funktionen und Sphäroidfunktionen, Berlin, Springer, 1954.
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.
National Bureau of Standards,Tables Relating to Mathieu Functions, New York, Columbia University Press, 1951.
Hanan Rubin,Anecdote on power series expansions of Mathieu functions, J. Math. and Phys., No. 4, pp. 339–341, 1964.
A. Weinstein, Memorial Sc. Math. No. 88, 1937.
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.
A. Weinstein,Some numerical results in intermediate problems for eigenvalues, Proc. of the Conference on Numerical Analysis, University of Maryland, May 1965.
E. T. Whittaker and G. N. Watson,Modern Analysis, Cambridge, University Press, fourth edition (1927). reprinted in 1963.
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Blanch, G. Numerical aspects of Mathieu eigenvalues. Rend. Circ. Mat. Palermo 15, 51–97 (1966). https://doi.org/10.1007/BF02849408
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DOI: https://doi.org/10.1007/BF02849408