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Formula:DLMF:25.12:E7 - Revision history
2024-03-29T14:23:14Z
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https://drmf-beta.wmflabs.org/index.php?title=Formula:DLMF:25.12:E7&diff=2362&oldid=prev
imported>SeedBot: DRMF
2017-03-05T22:34:48Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:DLMF:25.12:E7}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:DLMF:25.12:E6|Formula:DLMF:25.12:E6]] </div><br />
<div id="aligncenter"> [[Polylogarithms#DLMF:25.12:E7|formula in Polylogarithms]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.12:E8|Formula:DLMF:25.12:E8]] >> </div><br />
</div><br />
<br />
<br /><div align="center"><math>{\displaystyle <br />
\Dilogarithm@{\expe^{\iunit\theta}}<br />
= \sum_{n=1}^\infty \frac{\cos@{n \theta}}{n^2}<br />
+ \iunit \sum_{n=1}^\infty \frac{\sin@{n \theta}}{n^2}<br />
}</math></div><br />
<br />
== Constraint(s) ==<br />
<br />
<div align="left"><math>{\displaystyle 0 \leq \theta \leq 2\cpi}</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/25.12#E1 <math>{\displaystyle \mathrm{Li}_2}</math>]</span> : dilogarithm : [http://dlmf.nist.gov/25.12#E1 http://dlmf.nist.gov/25.12#E1]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/4.2.E11 <math>{\displaystyle \mathrm{e}}</math>]</span> : the base of the natural logarithm : [http://dlmf.nist.gov/4.2.E11 http://dlmf.nist.gov/4.2.E11]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/1.9.i <math>{\displaystyle \mathrm{i}}</math>]</span> : imaginary unit : [http://dlmf.nist.gov/1.9.i http://dlmf.nist.gov/1.9.i]<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/4.14#E2 <math>{\displaystyle \mathrm{cos}}</math>]</span> : cosine function : [http://dlmf.nist.gov/4.14#E2 http://dlmf.nist.gov/4.14#E2]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/4.14#E1 <math>{\displaystyle \mathrm{sin}}</math>]</span> : sine function : [http://dlmf.nist.gov/4.14#E1 http://dlmf.nist.gov/4.14#E1]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/5.19.E4 <math>{\displaystyle \pi}</math>]</span> : ratio of a circle's circumference to its diameter : [http://dlmf.nist.gov/5.19.E4 http://dlmf.nist.gov/5.19.E4]<br />
<br /><br />
<br />
== Bibliography==<br />
<br />
<span class="plainlinks">[HTTP://DLMF.NIST.GOV/25.12#E7 Equation (7), Section 25.12]</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:25.12:E6|Formula:DLMF:25.12:E6]] </div><br />
<div id="aligncenter"> [[Polylogarithms#DLMF:25.12:E7|formula in Polylogarithms]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.12:E8|Formula:DLMF:25.12:E8]] >> </div><br />
</div></div>
imported>SeedBot