29 Lamé FunctionsLamé Functions29.3 Definitions and Basic Properties29.5 Special Cases and Limiting Forms

§29.4 Graphics

ⓘ

Permalink:

http://dlmf.nist.gov/29.4

See also:

Annotations for Ch.29

Contents

1. §29.4(i) Eigenvalues of Lamé’s Equation: Line Graphs
2. §29.4(ii) Eigenvalues of Lamé’s Equation: Surfaces
3. §29.4(iii) Lamé Functions: Line Graphs
4. §29.4(iv) Lamé Functions: Surfaces

§29.4(i) Eigenvalues of Lamé’s Equation: Line Graphs

ⓘ

Keywords:

Lamé functions, eigenvalues, graphics

Notes:

These graphs were produced at NIST.

Permalink:

http://dlmf.nist.gov/29.4.i

See also:

Annotations for §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $m$: nonnegative integer and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F1

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F2

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $m$: nonnegative integer and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F3

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $m$: nonnegative integer and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F4

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $m$: nonnegative integer and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F5

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F6

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F7

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $m$: nonnegative integer and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F8

Encodings:

pdf, png

See also:

Annotations for §29.4(i), §29.4 and Ch.29

§29.4(ii) Eigenvalues of Lamé’s Equation: Surfaces

ⓘ

Keywords:

Lamé functions, eigenvalues, graphics

Notes:

These surfaces were produced at NIST.

Permalink:

http://dlmf.nist.gov/29.4.ii

See also:

Annotations for §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $k$: real parameter and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F9

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(ii), §29.4 and Ch.29

ⓘ

Symbols:

$b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $k$: real parameter and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F10

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(ii), §29.4 and Ch.29

ⓘ

Symbols:

$a_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $k$: real parameter and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F11

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(ii), §29.4 and Ch.29

ⓘ

Symbols:

$b_{\nu }^n\left(k^2\right)$: eigenvalues of Lamé’s equation, $k$: real parameter and $\nu$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F12

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(ii), §29.4 and Ch.29

§29.4(iii) Lamé Functions: Line Graphs

ⓘ

Keywords:

Lamé functions, graphics

Notes:

These graphs were produced at NIST.

Permalink:

http://dlmf.nist.gov/29.4.iii

See also:

Annotations for §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F13

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F14

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F15

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F16

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F17

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F18

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F19

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F20

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F21

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F22

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F23

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $K\left(k\right)$: Legendre’s complete elliptic integral of the first kind, $m$: nonnegative integer, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F24

Encodings:

pdf, png

See also:

Annotations for §29.4(iii), §29.4 and Ch.29

§29.4(iv) Lamé Functions: Surfaces

ⓘ

Keywords:

Lamé functions, graphics

Notes:

These surfaces were produced at NIST.

Permalink:

http://dlmf.nist.gov/29.4.iv

See also:

Annotations for §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F25

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F26

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F27

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F28

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F29

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F30

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑐}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F31

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

ⓘ

Symbols:

${\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)$: Lamé function, $x$: real variable and $k$: real parameter

Permalink:

http://dlmf.nist.gov/29.4.F32

Encodings:

Vizualization, pdf, png

See also:

Annotations for §29.4(iv), §29.4 and Ch.29

29.3 Definitions and Basic Properties29.5 Special Cases and Limiting Forms

© 2010–2025 NIST / Disclaimer / Feedback; Version 1.2.4; Release date 2025-03-15.

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy