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Difference between revisions of "Euler means"

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The means
 
The means
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e120/e120220/e1202201.png" /></td> </tr></table>
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$$\frac{1}{(q+1)^{n+1}}\sum_{k=0}^n\binom nkq^{n-k}S_k,\quad S_k=\sum_{n=0}^ka_n,$$
  
often for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e120/e120220/e1202202.png" />, used in the [[Euler summation method|Euler summation method]].
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often for $q=1$, used in the [[Euler summation method|Euler summation method]].

Latest revision as of 14:11, 23 July 2014

The means

$$\frac{1}{(q+1)^{n+1}}\sum_{k=0}^n\binom nkq^{n-k}S_k,\quad S_k=\sum_{n=0}^ka_n,$$

often for $q=1$, used in the Euler summation method.

How to Cite This Entry:
Euler means. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_means&oldid=32529
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article