File:Associated legendre functions 4.svg
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Summary[edit]
DescriptionAssociated legendre functions 4.svg |
English: A nice plot of the first associated legendre functions (associated legendre polynomials). Negative values for are not included. The functions are normalized to fit into the plot. |
Date | |
Source | Own work |
Author | Geek3 |
Mathematical Function Plot | |
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Description | Plot of the first associated legendre polynomials |
Equation1 | |
Coordinate System | Cartesian |
X Range | -1 .. 1 |
Y Range | -1 .. 1 |
Accuracy | 0.000001 units |
Equations[edit]
Normalisation[edit]
All functions were normalized the following way:
Licensing[edit]
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:44, 21 November 2009 | 640 × 540 (20 KB) | Geek3 (talk | contribs) | normalized associated legendre functions |
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Short title | Normalized Associated Legendre Functions - a nice plot of the Associated Legendre Functions |
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Image title |
Associated Legendre Functions from Wikimedia Commons P(0, 0, x) = 1 P(1, 0, x) = x P(1, 1, x) = -sqrt( 1 - x² ) P(2, 0, x) = ( 3x² - 1 ) / 2 P(2, 1, x) = -3x * sqrt( 1 - x² ) P(2, 2, x) = 3 * (1 - x²) P(3, 0, x) = ( 5x³ - 3x) / 2 P(3, 1, x) = 3/2 * ( 5x² - 1 ) * sqrt( 1 - x² ) P(3, 2, x) = 15x * ( x² - 1 ) P(3, 3, x) = 15 * ( x² - 1 ) * sqrt( 1 - x² ) P(4, 0, x) = ( 35x⁴ - 30x² + 3 ) / 8 P(4, 1, x) = 5/2 * ( 7x³ - 3x ) * sqrt( 1 - x² ) P(4, 2, x) = 15/2 * ( 7x² - 1 ) * ( 1 - x² ) P(4, 3, x) = 105 * x * ( x² - 1 ) * sqrt( 1 - x² ) P(4, 4, x) = 105 * ( 1 - x² ) * ( 1 - x² ) normalized by P(l, m, x) *= sqrt( int_-1^1( P(l, 0, x) ) / int_-1^1( P(l, m, x) ) ) plotted with cubic bezier-curves the bezier-controllpoints are calculated to give a very accurate result. Accuracy is 0.000001 units created with a plain text editor using GNU/Linux about: http://commons.wikimedia.org/wiki/Image:Associated_legendre_functions_4.svg source: http://commons.wikimedia.org/ rights: GNU Free Documentation license, Creative Commons Attribution ShareAlike license |