28 Mathieu Functions and Hill’s EquationMathieu Functions of Integer Order28.2 Definitions and Basic Properties28.4 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

1. §28.3(i) Line Graphs: Mathieu Functions with Fixed $q$ and Variable $x$
2. §28.3(ii) Surfaces: Mathieu Functions with Variable $x$ and $q$

§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

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Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

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Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

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Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

ⓘ

Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

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Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

ⓘ

Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

ⓘ

Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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

ⓘ

Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $n$: integer and $x$: 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 $x$ 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

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Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter and $x$: 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

ⓘ

Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter and $x$: 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

ⓘ

Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter and $x$: 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

ⓘ

Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter and $x$: 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

ⓘ

Symbols:

${\mathrm{ce}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter and $x$: 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 Properties28.4 Fourier Series

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