Stokes parameters: Difference between revisions

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→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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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]].
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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]]

Revision as of 23:31, 9 February 2014

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 :).
I have two sister. I love Backpacking, watching movies and Baton twirling.

My site ... Fifa 15 Coin Generator [Www.Sk-Goelk.At]

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