Mathieu equation

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31: Bibliography S

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The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order. ACM Trans. Math. Software 19 (3), pp. 377–390.

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ISSN 0098-3500, Document, ZentralBlatt

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item (e).

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Algorithm 721: MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu’s differential equation for noninteger and integer order. ACM Trans. Math. Software 19 (3), pp. 391–406.

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Notes:

Double-precision Fortran, maximum accuracy 18D

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ISSN 0098-3500, Document, GAMS (module 721; package TOMS), ZentralBlatt

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3rd item, 5th item.

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On the double points of a Mathieu equation. J. Comput. Appl. Math. 107 (1), pp. 111–125.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

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§28.7.

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Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

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ZentralBlatt

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§28.8(ii).

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32: Bibliography M

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The characteristic numbers of the Mathieu equation with purely imaginary parameter. Phil. Mag. Series 7 8 (53), pp. 834–840.

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Document, ZentralBlatt

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§28.7.

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33: Bibliography H

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The eigenvalues of Mathieu’s equation and their branch points. Stud. Appl. Math. 64 (2), pp. 113–141.

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ISSN 0022-2526, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§28.7.

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34: Bibliography B

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Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values. U.S. Government Printing Office, Washington, D.C..

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MathReview (John Todd), ZentralBlatt

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1st item.

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Table of characteristic values of Mathieu’s equation for large values of the parameter. J. Washington Acad. Sci. 45 (6), pp. 166–196.

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MathReview (L. Fox)

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3rd item.

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35: Bibliography C

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Théorie Générale de L’Équation de Mathieu et de quelques autres Équations différentielles de la mécanique. Masson et Cie, Paris (French).

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MathReview (A. Erdélyi), ZentralBlatt

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§28.1, Notations C, Notations I, Notations I, Notations J, Notations J, Notations S.

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Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation. Comm. ACM 12 (7), pp. 399–407.

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Notes:

Includes double-precision Fortran program, maximum accuracy 13D.

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ISSN 0001-0782, Document

Referenced by:

§28.36(ii), §28.36(iii).

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36: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For example, replacing $2q\cos (2z)$ of (28.2.1) by $\lambda \cos (2\pi \alpha n+\theta )$, $n\in \mathbb{Z}$ gives an almost Mathieu equation which for appropriate $\alpha$ has such properties. …

37: Bibliography F

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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice. Phys. A 190 (3-4), pp. 346–362.

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ISSN 0378-4371, Document, MathReview

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6th item.

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38: Bibliography

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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.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§28.1, §28.1, §28.10(i), §28.11, §28.12(ii), §28.17, §28.2(ii), §28.2(iii), §28.2(iv), §28.28(i), §28.28(ii), §28.29(i), §28.32(i), §28.32(ii), §28.4(i), §28.5(i), Ch.28, §29.1, §29.11, §29.12(i), §29.12(ii), §29.12(iii), §29.14, §29.15(ii), §29.15(ii), §29.17(i), §29.18(iii), Ch.29, §30.1, §30.10, §30.11(i), §30.11(vi), §30.2(ii), §30.4(iii), §30.6, §30.8(i), §30.8(ii), Ch.30, §31.4, §31.5, §31.9(ii), Notations F, Notations G, Notations M, Notations N.

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39: 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 28–30.

40: Software Index

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	Open Source													With Book						Commercial
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28 Mathieu Functions and Hill’s Equation
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