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28 Mathieu Functions and Hill’s Equation Mathieu Functions of Noninteger Order 28.12 Definitions and Basic Properties 28.14 Fourier Series

§28.13 Graphics

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Keywords:: Mathieu functions, graphics
Permalink:: http://dlmf.nist.gov/28.13
See also:: Annotations for Ch.28

Contents

§28.13(i) Eigenvalues $\lambda_{\nu}\left(q\right)$ for General $\nu$
§28.13(ii) Solutions $\operatorname{ce}_{\nu}\left(x,q\right)$ , $\operatorname{se}_{\nu}\left(x,q\right)$ , and $\operatorname{me}_{\nu}\left(x,q\right)$ for General $\nu$

§28.13(i) Eigenvalues $\lambda_{\nu}\left(q\right)$ for General $\nu$

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Keywords:: Mathieu’s equation, eigenvalues (or characteristic values), graphics
Notes:: Figures 28.13.1 and 28.13.2 were produced at NIST.
Permalink:: http://dlmf.nist.gov/28.13.i
See also:: Annotations for §28.13 and Ch.28

See accompanying text — Figure 28.13.1: $\lambda_{\nu}\left(q\right)$ as a function of $q$ for $\nu=0.5(1)3.5$ and $a_{n}\left(q\right),b_{n}\left(q\right)$ for $n=0,1,2,3,4$ ( $a$ ’s), $n=1,2,3,4$ ( $b$ ’s). (Compare Figure 28.2.1.) Magnify 3D Help

See accompanying text — Figure 28.13.1: $\lambda_{\nu}\left(q\right)$ as a function of $q$ for $\nu=0.5(1)3.5$ and $a_{n}\left(q\right),b_{n}\left(q\right)$ for $n=0,1,2,3,4$ ( $a$ ’s), $n=1,2,3,4$ ( $b$ ’s). (Compare Figure 28.2.1.) Magnify 3D Help

§28.13(ii) Solutions $\operatorname{ce}_{\nu}\left(x,q\right)$ , $\operatorname{se}_{\nu}\left(x,q\right)$ , and $\operatorname{me}_{\nu}\left(x,q\right)$ for General $\nu$

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Notes:: Figures 28.13.3–28.13.5 were produced at NIST.
Permalink:: http://dlmf.nist.gov/28.13.ii
See also:: Annotations for §28.13 and Ch.28

See accompanying text — Figure 28.13.3: $\operatorname{ce}_{\nu}\left(x,1\right)$ for $-1<\nu<1$ , $0\leq x\leq 2\pi$ . Magnify 3D Help

See accompanying text — Figure 28.13.3: $\operatorname{ce}_{\nu}\left(x,1\right)$ for $-1<\nu<1$ , $0\leq x\leq 2\pi$ . Magnify 3D Help

See accompanying text — Figure 28.13.5: $\operatorname{me}_{\mathrm{i}\mu}\left(x,1\right)$ for $0.1\leq\mu\leq 0.4$ , $-\pi\leq x\leq\pi.$ Magnify 3D Help

28.12 Definitions and Basic Properties 28.14 Fourier Series

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