Digital Library of Mathematical Functions
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28 Mathieu Functions and Hill’s EquationMathieu Functions of Integer Order

§28.3 Graphics

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

Even \pi-Periodic Solutions

See accompanying text
Figure 28.3.1: \mathop{\mathrm{ce}_{{2n}}\/}\nolimits\!\left(x,1\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify
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Symbols:
\mathop{\mathrm{ce}_{{n}}\/}\nolimits\!\left(z,q\right): Mathieu function, n: integer and x: real variable
Referenced by:
§28.3(i)
Permalink:
http://dlmf.nist.gov/28.3.F1
Encodings:
pdf, png
See accompanying text
Figure 28.3.2: \mathop{\mathrm{ce}_{{2n}}\/}\nolimits\!\left(x,10\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify

Even \pi-Antiperiodic Solutions

See accompanying text
Figure 28.3.3: \mathop{\mathrm{ce}_{{2n+1}}\/}\nolimits\!\left(x,1\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify
See accompanying text
Figure 28.3.4: \mathop{\mathrm{ce}_{{2n+1}}\/}\nolimits\!\left(x,10\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify

Odd \pi-Antiperiodic Solutions

See accompanying text
Figure 28.3.5: \mathop{\mathrm{se}_{{2n+1}}\/}\nolimits\!\left(x,1\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify
See accompanying text
Figure 28.3.6: \mathop{\mathrm{se}_{{2n+1}}\/}\nolimits\!\left(x,10\right) for 0\leq x\leq\pi/2, n=0,1,2,3. Magnify

Odd \pi-Periodic Solutions

See accompanying text
Figure 28.3.7: \mathop{\mathrm{se}_{{2n}}\/}\nolimits\!\left(x,1\right) for 0\leq x\leq\pi/2, n=1,2,3,4. Magnify
See accompanying text
Figure 28.3.8: \mathop{\mathrm{se}_{{2n}}\/}\nolimits\!\left(x,10\right) for 0\leq x\leq\pi/2, n=1,2,3,4. Magnify
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Symbols:
\mathop{\mathrm{se}_{{n}}\/}\nolimits\!\left(z,q\right): Mathieu function, n: integer and x: real variable
Referenced by:
§28.3(i)
Permalink:
http://dlmf.nist.gov/28.3.F8
Encodings:
pdf, png

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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Notes:
Figures 28.3.9–28.3.13 were produced at NIST.
Keywords:
Mathieu functions
Permalink:
http://dlmf.nist.gov/28.3.ii
See accompanying text
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Figure 28.3.9: \mathop{\mathrm{ce}_{{0}}\/}\nolimits\!\left(x,q\right) for 0\leq x\leq 2\pi, 0\leq q\leq 10. Magnify
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Symbols:
\mathop{\mathrm{ce}_{{n}}\/}\nolimits\!\left(z,q\right): Mathieu function, q=h^{2}: parameter and x: real variable
Referenced by:
§28.3(ii)
Permalink:
http://dlmf.nist.gov/28.3.F9
Encodings:
VRML, X3D, pdf, png
See accompanying text
Visualization Help
Figure 28.3.10: \mathop{\mathrm{se}_{{1}}\/}\nolimits\!\left(x,q\right) for 0\leq x\leq 2\pi, 0\leq q\leq 10. Magnify
See accompanying text
Visualization Help
Figure 28.3.11: \mathop{\mathrm{ce}_{{1}}\/}\nolimits\!\left(x,q\right) for 0\leq x\leq 2\pi, 0\leq q\leq 10. Magnify
See accompanying text
Visualization Help
Figure 28.3.12: \mathop{\mathrm{se}_{{2}}\/}\nolimits\!\left(x,q\right) for 0\leq x\leq 2\pi, 0\leq q\leq 10. Magnify
See accompanying text
Visualization Help
Figure 28.3.13: \mathop{\mathrm{ce}_{{2}}\/}\nolimits\!\left(x,q\right) for 0\leq x\leq 2\pi, 0\leq q\leq 10. Magnify
Show Annotations
Symbols:
\mathop{\mathrm{ce}_{{n}}\/}\nolimits\!\left(z,q\right): Mathieu function, q=h^{2}: parameter and x: real variable
Referenced by:
§28.3(ii)
Permalink:
http://dlmf.nist.gov/28.3.F13
Encodings:
VRML, X3D, pdf, png
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