https://drmf-beta.wmflabs.org/index.php?title=Formula:DLMF:25.15:E5&feed=atom&action=history
Formula:DLMF:25.15:E5 - Revision history
2024-03-29T01:21:28Z
Revision history for this page on the wiki
MediaWiki 1.42.0-wmf.12
https://drmf-beta.wmflabs.org/index.php?title=Formula:DLMF:25.15:E5&diff=2669&oldid=prev
Move page script: Move page script moved page Formula:DLMF:25.15:E5 to F:DLMF:25.15:E5
2019-12-22T06:33:11Z
<p>Move page script moved page <a href="/wiki/Formula:DLMF:25.15:E5" title="Formula:DLMF:25.15:E5">Formula:DLMF:25.15:E5</a> to <a href="/index.php?title=F:DLMF:25.15:E5&action=edit&redlink=1" class="new" title="F:DLMF:25.15:E5 (page does not exist)">F:DLMF:25.15:E5</a></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<tr class="diff-title" lang="en">
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:33, 22 December 2019</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>
Move page script
https://drmf-beta.wmflabs.org/index.php?title=Formula:DLMF:25.15:E5&diff=2386&oldid=prev
imported>SeedBot: DRMF
2017-03-05T22:34:49Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:DLMF:25.15:E5}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:DLMF:25.15:E4|Formula:DLMF:25.15:E4]] </div><br />
<div id="aligncenter"> [[Dirichlet_L-functions#DLMF:25.15:E5|formula in Dirichlet L-functions]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.15:E7|Formula:DLMF:25.15:E7]] >> </div><br />
</div><br />
<br />
<br /><div align="center"><math>{\displaystyle <br />
\DirichletL@{1-s}{\chi}<br />
= \frac{k^{s-1} \EulerGamma@{s}}{(2 \cpi)^s}<br />
\* {\left( \expe^{-\cpi \iunit s/2} + \chi(-1) \expe^{\cpi \iunit s/2} \right)}<br />
\* G(\chi) \DirichletL@{s}{\overline{\chi}}<br />
}</math></div><br />
<br />
== Substitution(s) ==<br />
<br />
<div align="left"><math>{\displaystyle {\displaystyle G(\chi) = \sum_{r=1}^k \chi(r) \expe^{2 \cpi \iunit r/k}}}</math></div><br /><br />
<br />
== Constraint(s) ==<br />
<br />
<div align="left"><math>{\displaystyle \chi}</math> is a primitive character (mod <math>{\displaystyle k}</math>) &<br /><br />
<math>{\displaystyle \overline{\chi}}</math> is the complex conjugate of <math>{\displaystyle \chi}</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 />
& : logical and<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/25.15#E1 <math>{\displaystyle L}</math>]</span> : Dirichlet <math>{\displaystyle \DirichletL}</math>-function : [http://dlmf.nist.gov/25.15#E1 http://dlmf.nist.gov/25.15#E1]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/5.2#E1 <math>{\displaystyle \Gamma}</math>]</span> : Euler's gamma function : [http://dlmf.nist.gov/5.2#E1 http://dlmf.nist.gov/5.2#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 />
<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 /><br />
<br />
== Bibliography==<br />
<br />
<span class="plainlinks">[HTTP://DLMF.NIST.GOV/25.15#E5 Equation (5), Section 25.15]</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:25.15:E4|Formula:DLMF:25.15:E4]] </div><br />
<div id="aligncenter"> [[Dirichlet_L-functions#DLMF:25.15:E5|formula in Dirichlet L-functions]] </div><br />
<div id="alignright"> [[Formula:DLMF:25.15:E7|Formula:DLMF:25.15:E7]] >> </div><br />
</div></div>
imported>SeedBot