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DLMF: §28.3 Graphics ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation

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28 Mathieu Functions and Hill’s Equation Mathieu Functions of Integer Order 28.2 Definitions and Basic Properties 28.4 Fourier Series

§28.3 Graphics

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Keywords:: Mathieu functions, graphics
Permalink:: http://dlmf.nist.gov/28.3
See also:: Annotations for Ch.28

Contents

§28.3(i) Line Graphs: Mathieu Functions with Fixed $q$ and Variable $x$

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Notes:: Figures 28.3.1–28.3.8 were produced at NIST.
Permalink:: http://dlmf.nist.gov/28.3.i
See also:: Annotations for §28.3 and Ch.28

Even $\pi$ -Periodic Solutions

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See also:: Annotations for §28.3(i), §28.3 and Ch.28

See accompanying text — Figure 28.3.1: $\operatorname{ce}_{2n}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

See accompanying text — Figure 28.3.1: $\operatorname{ce}_{2n}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

Even $\pi$ -Antiperiodic Solutions

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See also:: Annotations for §28.3(i), §28.3 and Ch.28

See accompanying text — Figure 28.3.3: $\operatorname{ce}_{2n+1}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

See accompanying text — Figure 28.3.3: $\operatorname{ce}_{2n+1}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

Odd $\pi$ -Antiperiodic Solutions

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See also:: Annotations for §28.3(i), §28.3 and Ch.28

See accompanying text — Figure 28.3.5: $\operatorname{se}_{2n+1}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

See accompanying text — Figure 28.3.5: $\operatorname{se}_{2n+1}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=0,1,2,3$ . Magnify

Odd $\pi$ -Periodic Solutions

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See also:: Annotations for §28.3(i), §28.3 and Ch.28

See accompanying text — Figure 28.3.7: $\operatorname{se}_{2n}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=1,2,3,4$ . Magnify

See accompanying text — Figure 28.3.7: $\operatorname{se}_{2n}\left(x,1\right)$ for $0\leq x\leq\pi/2$ , $n=1,2,3,4$ . Magnify

For further graphs see Jahnke et al. (1966, pp. 264–265 and 268–275).

§28.3(ii) Surfaces: Mathieu Functions with Variable $x$ and $q$

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Keywords:: Mathieu functions, graphics
Notes:: Figures 28.3.9–28.3.13 were produced at NIST.
Permalink:: http://dlmf.nist.gov/28.3.ii
See also:: Annotations for §28.3 and Ch.28

See accompanying text — Figure 28.3.9: $\operatorname{ce}_{0}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

See accompanying text — Figure 28.3.9: $\operatorname{ce}_{0}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

See accompanying text — Figure 28.3.11: $\operatorname{ce}_{1}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

See accompanying text — Figure 28.3.11: $\operatorname{ce}_{1}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

See accompanying text — Figure 28.3.13: $\operatorname{ce}_{2}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

28.2 Definitions and Basic Properties 28.4 Fourier Series

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