https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Intersection_curve 2026-05-21T05:01:51Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Intersection_curve&diff=30327&oldid=prev 2014-01-24T16:42:08Z

<p>links fixed</p> <p><b>New page</b></p><div>{{orphan|date=January 2014}}<br /> <br /> In mathematics, &#039;&#039;&#039;Hölder summation&#039;&#039;&#039; is a method for summing [[divergent series]] introduced by {{harvs|txt|last=Hölder|year=1882|authorlink=Otto Hölder}}.<br /> <br /> ==Definition==<br /> <br /> Given a [[series (mathematics)|series]]<br /> :&lt;math&gt; a_1+a_2+\cdots, \, &lt;/math&gt;<br /> define<br /> :&lt;math&gt;H^0_n=a_1+a_2+\cdots+a_n \, &lt;/math&gt;<br /> :&lt;math&gt;H^{k+1}_n=\frac{H^k_1+\cdots+H^k_n}{n}&lt;/math&gt;<br /> If the limit<br /> :&lt;math&gt;\lim_{n\rightarrow\infty}H^k_n \, &lt;/math&gt;<br /> exists for some &#039;&#039;k&#039;&#039;, this is called the Hölder sum, or the (&#039;&#039;H&#039;&#039;,&#039;&#039;k&#039;&#039;) sum, of the series.<br /> <br /> ==References==<br /> <br /> *{{citation|first=O.|last= Hölder|authorlink=Otto Hölder|title=Grenzwerthe von Reihen an der Konvergenzgrenze|journal= Math. Ann. |volume= 20 |year=1882|pages= 535–549}}<br /> <br /> *{{eom|id=Hölder_summation_methods|title=Hölder summation methods}}<br /> <br /> {{DEFAULTSORT:Holder Summation}}<br /> [[Category:Summability methods]]</div>

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