Stokes parameters - Revision history

en>Phleg1: dab

2014-10-23T07:49:54Z

dab

← Older revision		Revision as of 09:49, 23 October 2014
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en>LutzL: /* Definitions */ aligned not supported in texvc, uses align instead

2014-02-09T22:31:40Z

Definitions: aligned not supported in texvc, uses align instead

← Older revision		Revision as of 00:31, 10 February 2014
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	~~In [[mathematics]], there are several functions known as '''Kummer~~'s ~~function~~''~~'. One is known as~~ the ~~[[confluent hypergeometric function]] of Kummer. Another one, defined below, is related to~~ the ~~[[polylogarithm]]. Both are named~~ for ~~[[Ernst Kummer]]~~.		My name's Garrett Kindel but everybody calls me Garrett. I'm from United States. I'm studying at the college (1st year) and I play the Banjo for 6 years. Usually I choose songs from my famous films :). <br>I have two sister. I love Backpacking, watching movies and Baton twirling.<br><br>My site ... Fifa 15 Coin Generator [[http://www.sk-goelk.at/index.php?option=com_easybookreloaded& Www.Sk-Goelk.At]]

	~~Kummer's function is defined by~~

	:<~~math~~>~~\Lambda_n(z)=\int_0^z \frac{\log^{n-1}\|t\|}{1+t}\;dt~~.<~~/math~~>

	~~The~~ [[~~duplication formula]] is~~

	:~~<math>\Lambda_n(z)+\Lambda_n(-z)= 2^{1-n}\Lambda_n(-z^2)<~~/~~math>~~.

	~~Compare this to the duplication formula for the polylogarithm:~~

	~~:<math>\operatorname{Li}_n(z)+\operatorname{Li}_n(-z)= 2^{1~~-~~n}\operatorname{Li}_n(z^2)~~.</~~math>~~

	~~An explicit link to the polylogarithm is given by~~

	~~:<math>\operatorname{Li}_n(z)=\operatorname{Li}_n(1)\;\;+\;\;~~
	~~\sum_{k~~=~~1}^{n-1} (-)^{k-1} \;\frac{\log^k \|z\|} {k!} \;\operatorname{Li}_{n-k} (z) \;\;+\;\;~~
	~~\frac{(-)^{n-1}}{(n-1)!} \;\left[ \Lambda_n(-1) - \Lambda_n(-z) \right]~~.~~</math>~~

	~~==References==~~
	*{{citation\|editor-first=Leonard\|editor-~~last=Lewin\|title=Structural Properties of Polylogarithms\|year=1991\|location=Providence, RI\|publisher=American Mathematical Society\|isbn=0-8218-4532-2}}~~.

	~~[[Category:Special functions]]~~

	~~{{mathanalysis-stub}}~~

	~~[[hu:Kummer-függvény~~]]

67.168.77.27: /* Definitions */ Square of averages -> Average of squares. (an easy way of seeing this is right is that the average of the fields is zero, so I = Q = U = V = 0 under the previous definitiion)

2013-11-30T00:59:00Z

Definitions: Square of averages -> Average of squares. (an easy way of seeing this is right is that the average of the fields is zero, so I = Q = U = V = 0 under the previous definitiion)

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en>BenFrantzDale: /* Examples */

2012-05-16T17:40:13Z

Examples

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