Goldstein’s

H. P. Mulholland and S. Goldstein (1929) The characteristic numbers of the Mathieu equation with purely imaginary parameter. Phil. Mag. Series 7 8 (53), pp. 834–840.

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External Links:: Document, ZentralBlatt
Referenced by:: §28.7.
Encodings:: BibTeX

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5: 28.7 Analytic Continuation of Eigenvalues

§28.7 Analytic Continuation of Eigenvalues

… ►The normal values are simple roots of the corresponding equations (28.2.21) and (28.2.22). …See also Mulholland and Goldstein (1929), Bouwkamp (1948), Meixner et al. (1980), Hunter and Guerrieri (1981), Hunter (1981), and Shivakumar and Xue (1999). … ► … ►

28.7.4

\sum_{n=0}^{\infty}\left(b_{2n+2}\left(q\right)-(2n+2)^{2}\right)=0.

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Symbols:: $b_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation, $q=h^{2}$ : parameter and $n$ : integer
Permalink:: http://dlmf.nist.gov/28.7.E4
Encodings:: pMML, png, TeX
See also:: Annotations for §28.7 and Ch.28

Goldstein’s

5 matching pages

1: 28.26 Asymptotic Approximations for Large q

§28.26(i) Goldstein’s Expansions

2: 28.8 Asymptotic Expansions for Large q

§28.8(iii) Goldstein’s Expansions

3: Bibliography G

4: Bibliography M

5: 28.7 Analytic Continuation of Eigenvalues

§28.7 Analytic Continuation of Eigenvalues

1: 28.26 Asymptotic Approximations for Large $q$

2: 28.8 Asymptotic Expansions for Large $q$