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Formula:DLMF:25.16:E11 - Revision history
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imported>SeedBot: DRMF
2017-03-05T22:34:50Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:DLMF:25.16:E11}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:DLMF:25.16:E10|Formula:DLMF:25.16:E10]] </div><br />
<div id="aligncenter"> [[Mathematical_Applications#DLMF:25.16:E11|formula in Mathematical Applications]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.16:E12|Formula:DLMF:25.16:E12]] >> </div><br />
</div><br />
<br />
<br /><div align="center"><math>{\displaystyle <br />
\GenEulerSumH@{s}{z}<br />
= \sum_{n=1}^\infty \frac{1}{n^s} \sum_{m=1}^n \frac{1}{m^z}<br />
}</math></div><br />
<br />
== Constraint(s) ==<br />
<br />
<div align="left"><math>{\displaystyle \realpart{(s+z)} > 1}</math></div><br /><br />
<br />
== Note(s) ==<br />
<br />
<div align="left"><math>{\displaystyle \EulerSumH@{s}}</math> is the special case <math>{\displaystyle \GenEulerSumH@{s}{1}}</math> of <math>{\displaystyle \GenEulerSumH@{s}{z}}</math></div><br /><br />
<br />
== Proof ==<br />
<br />
We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.<br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://dlmf.nist.gov/25.16#SS2.p7 <math>{\displaystyle H}</math>]</span> : generalized Euler sums : [http://dlmf.nist.gov/25.16#SS2.p7 http://dlmf.nist.gov/25.16#SS2.p7]<br /><br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:sum <math>{\displaystyle \Sigma}</math>]</span> : sum : [http://drmf.wmflabs.org/wiki/Definition:sum http://drmf.wmflabs.org/wiki/Definition:sum]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/1.9#E2 <math>{\displaystyle \Re {z}}</math>]</span> : real part : [http://dlmf.nist.gov/1.9#E2 http://dlmf.nist.gov/1.9#E2]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/25.16#SS2.p1 <math>{\displaystyle H}</math>]</span> : Euler sums : [http://dlmf.nist.gov/25.16#SS2.p1 http://dlmf.nist.gov/25.16#SS2.p1]<br />
<br /><br />
<br />
== Bibliography==<br />
<br />
<span class="plainlinks">[HTTP://DLMF.NIST.GOV/25.16#E11 Equation (11), Section 25.16]</span> of [[Bibliography#DLMF|'''DLMF''']].<br />
<br />
== URL links ==<br />
<br />
We ask users to provide relevant URL links in this space.<br />
<br />
<br /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Formula:DLMF:25.16:E10|Formula:DLMF:25.16:E10]] </div><br />
<div id="aligncenter"> [[Mathematical_Applications#DLMF:25.16:E11|formula in Mathematical Applications]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.16:E12|Formula:DLMF:25.16:E12]] >> </div><br />
</div></div>
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