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

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

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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 $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Referenced by:: §28.3(i)
Permalink:: http://dlmf.nist.gov/28.3.F1
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

See accompanying text

Figure 28.3.2: $\operatorname{ce}_{2n}\left(x,10\right)$ for $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F2
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

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 $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F3
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

See accompanying text

Figure 28.3.4: $\operatorname{ce}_{2n+1}\left(x,10\right)$ for $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F4
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

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 $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F5
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

See accompanying text

Figure 28.3.6: $\operatorname{se}_{2n+1}\left(x,10\right)$ for $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F6
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

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 $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F7
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

See accompanying text

Figure 28.3.8: $\operatorname{se}_{2n}\left(x,10\right)$ for $0\leq x\leq\pi/2$ ,

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, : integer and : real variable
Referenced by:: §28.3(i)
Permalink:: http://dlmf.nist.gov/28.3.F8
Encodings:: pdf, png
See also:: Annotations for §28.3(i), §28.3(i), §28.3 and Ch.28

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

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

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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

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, $q=h^{2}$ : parameter and : real variable
Referenced by:: §28.3(ii)
Permalink:: http://dlmf.nist.gov/28.3.F9
Encodings:: Vizualization, pdf, png
See also:: Annotations for §28.3(ii), §28.3 and Ch.28

See accompanying text

Figure 28.3.10: $\operatorname{se}_{1}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, $q=h^{2}$ : parameter and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F10
Encodings:: Vizualization, pdf, png
See also:: Annotations for §28.3(ii), §28.3 and Ch.28

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

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, $q=h^{2}$ : parameter and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F11
Encodings:: Vizualization, pdf, png
See also:: Annotations for §28.3(ii), §28.3 and Ch.28

See accompanying text

Figure 28.3.12: $\operatorname{se}_{2}\left(x,q\right)$ for $0\leq x\leq 2\pi$ , $0\leq q\leq 10$ . Magnify 3D Help

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Symbols:: $\operatorname{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, $q=h^{2}$ : parameter and : real variable
Permalink:: http://dlmf.nist.gov/28.3.F12
Encodings:: Vizualization, pdf, png
See also:: Annotations for §28.3(ii), §28.3 and Ch.28

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

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\pi$ : the ratio of the circumference of a circle to its diameter, $q=h^{2}$ : parameter and : real variable
Referenced by:: §28.3(ii)
Permalink:: http://dlmf.nist.gov/28.3.F13
Encodings:: Vizualization, pdf, png
See also:: Annotations for §28.3(ii), §28.3 and Ch.28

28.2 Definitions and Basic Properties 28.4 Fourier Series

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