§30.7 Graphics

Contents

• §30.7(i) Eigenvalues
• §30.7(ii) Functions of the First Kind
• §30.7(iii) Functions of the Second Kind
• §30.7(iv) Functions of Complex Argument

§30.7(i) Eigenvalues

ⓘ

Keywords:

eigenvalues, graphics, spheroidal differential equation

Notes:

Figures 30.7.1–30.7.4 were produced at NIST with the aid of Maple procedures provided by the author.

Permalink:

http://dlmf.nist.gov/30.7.i

See also:

Annotations for §30.7 and Ch.30

ⓘ

Symbols:

${\lambda }_n^m\left({\gamma }^2\right)$: eigenvalues of the spheroidal differential equation, $n\ge m$: integer degree and ${\gamma }^2$: real parameter

Referenced by:

§30.7(i)

Permalink:

http://dlmf.nist.gov/30.7.F1

Encodings:

pdf, png

See also:

Annotations for §30.7(i), §30.7 and Ch.30

ⓘ

Symbols:

${\lambda }_n^m\left({\gamma }^2\right)$: eigenvalues of the spheroidal differential equation, $n\ge m$: integer degree and ${\gamma }^2$: real parameter

Permalink:

http://dlmf.nist.gov/30.7.F2

Encodings:

pdf, png

See also:

Annotations for §30.7(i), §30.7 and Ch.30

ⓘ

Symbols:

${\lambda }_n^m\left({\gamma }^2\right)$: eigenvalues of the spheroidal differential equation, $n\ge m$: integer degree and ${\gamma }^2$: real parameter

Permalink:

http://dlmf.nist.gov/30.7.F3

Encodings:

pdf, png

See also:

Annotations for §30.7(i), §30.7 and Ch.30

ⓘ

Symbols:

${\lambda }_n^m\left({\gamma }^2\right)$: eigenvalues of the spheroidal differential equation, $n\ge m$: integer degree and ${\gamma }^2$: real parameter

Referenced by:

§30.7(i)

Permalink:

http://dlmf.nist.gov/30.7.F4

Encodings:

pdf, png

See also:

Annotations for §30.7(i), §30.7 and Ch.30

§30.7(ii) Functions of the First Kind

ⓘ

Keywords:

graphics, spheroidal wave functions

Notes:

Figures 30.7.5–30.7.10 were produced at NIST with the aid of Maple procedures provided by the author.

Permalink:

http://dlmf.nist.gov/30.7.ii

See also:

Annotations for §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and $n\ge m$: integer degree

Referenced by:

§30.7(ii)

Permalink:

http://dlmf.nist.gov/30.7.F5

Encodings:

pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F6

Encodings:

pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F7

Encodings:

pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F8

Encodings:

pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and ${\gamma }^2$: real parameter

Permalink:

http://dlmf.nist.gov/30.7.F9

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Ps}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the first kind, $x$: real variable and ${\gamma }^2$: real parameter

Referenced by:

§30.7(ii)

Permalink:

http://dlmf.nist.gov/30.7.F10

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(ii), §30.7 and Ch.30

§30.7(iii) Functions of the Second Kind

ⓘ

Notes:

Figures 30.7.11–30.7.15 were produced at NIST with the aid of Maple procedures provided by the author.

Permalink:

http://dlmf.nist.gov/30.7.iii

See also:

Annotations for §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Qs}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind, $x$: real variable and $n\ge m$: integer degree

Referenced by:

§30.7(iii)

Permalink:

http://dlmf.nist.gov/30.7.F11

Encodings:

pdf, png

See also:

Annotations for §30.7(iii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Qs}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F12

Encodings:

pdf, png

See also:

Annotations for §30.7(iii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Qs}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F13

Encodings:

pdf, png

See also:

Annotations for §30.7(iii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Qs}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind, $x$: real variable and $n\ge m$: integer degree

Permalink:

http://dlmf.nist.gov/30.7.F14

Encodings:

pdf, png

See also:

Annotations for §30.7(iii), §30.7 and Ch.30

ⓘ

Symbols:

${\mathsf{Qs}}_n^m(x,{\gamma }^2)$: spheroidal wave function of the second kind, $x$: real variable and ${\gamma }^2$: real parameter

Referenced by:

§30.7(iii)

Permalink:

http://dlmf.nist.gov/30.7.F15

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iii), §30.7 and Ch.30

§30.7(iv) Functions of Complex Argument

ⓘ

Keywords:

graphics, spheroidal wave functions

Notes:

Figures 30.7.16–30.7.21 were produced at NIST with the aid of Maple procedures provided by the author.

Referenced by:

§30.1

Permalink:

http://dlmf.nist.gov/30.7.iv

See also:

Annotations for §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Ps}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Referenced by:

§30.7(iv)

Permalink:

http://dlmf.nist.gov/30.7.F16

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Ps}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Permalink:

http://dlmf.nist.gov/30.7.F17

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Ps}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Permalink:

http://dlmf.nist.gov/30.7.F18

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Ps}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Permalink:

http://dlmf.nist.gov/30.7.F19

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Qs}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Permalink:

http://dlmf.nist.gov/30.7.F20

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, ${\mathit{Qs}}_n^m(z,{\gamma }^2)$: spheroidal wave function of complex argument, $x$: real variable and $y$: real variable

Referenced by:

§30.7(iv)

Permalink:

http://dlmf.nist.gov/30.7.F21

Encodings:

Vizualization, pdf, png

See also:

Annotations for §30.7(iv), §30.7 and Ch.30