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Definition:qcosKLS - Revision history
2024-03-28T08:21:40Z
Revision history for this page on the wiki
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Move page script: Move page script moved page Definition:qcosKLS to D:qcosKLS
2019-12-22T06:49:58Z
<p>Move page script moved page <a href="/wiki/Definition:qcosKLS" title="Definition:qcosKLS">Definition:qcosKLS</a> to <a href="https://www.wikidata.org/wiki/qcosKLS" class="extiw" title="d:qcosKLS">D:qcosKLS</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:49, 22 December 2019</td>
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imported>SeedBot: DRMF
2017-03-05T22:33:12Z
<p>DRMF</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:33, 5 March 2017</td>
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imported>SeedBot
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imported>SeedBot: DRMF
2017-03-05T22:32:21Z
<p>DRMF</p>
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<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 23:32, 5 March 2017</td>
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imported>SeedBot
https://drmf-beta.wmflabs.org/index.php?title=Definition:qcosKLS&diff=404&oldid=prev
imported>SeedBot: DRMF
2017-03-05T22:30:39Z
<p>DRMF</p>
<p><b>New page</b></p><div><div id="drmf_head"><br />
<div id="alignleft"> << [[Definition:qexpKLS|Definition:qexpKLS]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qMeixner|Definition:qMeixner]] >> </div><br />
</div><br />
The LaTeX DLMF and DRMF macro '''\qcosKLS''' represents a <math>q</math>-analogue of the <br />
<math>\cos</math> function:~<math>\qcosKLS{q}</math>.<br />
<br />
This macro is in the category of polynomials.<br />
<br />
In math mode, this macro can be called in the following ways:<br />
<br />
:'''\qcosKLS{q}''' produces <math>{\displaystyle \qcosKLS{q}}</math><br /><br />
:'''\qcosKLS{q}@{z}''' produces <math>{\displaystyle \qcosKLS{q}@{z}}</math><br /><br />
:'''\qcosKLS{q}@@{z}''' produces <math>{\displaystyle \qcosKLS{q}@@{z}}</math><br /><br />
<br />
These are defined by<br />
<math>{\displaystyle<br />
\qcosKLS{q}@{z}:=\frac{\qexpKLS{q}@{iz)+{\mathrm e}_q(-iz}}{2}=<br />
\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n}}{\qPochhammer{q}{q}{2n}}<br />
}</math><br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:qcosKLS <math>{\displaystyle \mathrm{cos}_{q}}</math>]</span> : <math>{\displaystyle q}</math>-analogue of the <math>{\displaystyle \cos}</math> function used in KLS: <math>{\displaystyle \cos_q}</math> : [http://drmf.wmflabs.org/wiki/Definition:qcosKLS http://drmf.wmflabs.org/wiki/Definition:qcosKLS]<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://drmf.wmflabs.org/wiki/Definition:qexpKLS <math>{\displaystyle \mathrm{e}_{q}}</math>]</span> : <math>{\displaystyle q}</math>-analogue of the <math>{\displaystyle \exp}</math> function used in KLS: <math>{\displaystyle \mathrm{e}_{q}}</math> : [http://drmf.wmflabs.org/wiki/Definition:qexpKLS http://drmf.wmflabs.org/wiki/Definition:qexpKLS]<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/5.18#i <math>{\displaystyle (a;q)_n}</math>]</span> : <math>{\displaystyle q}</math>-Pochhammer symbol : [http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/5.18#i] [http://dlmf.nist.gov/17.2#SS1.p1 http://dlmf.nist.gov/17.2#SS1.p1]<br />
<br /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Definition:qexpKLS|Definition:qexpKLS]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qMeixner|Definition:qMeixner]] >> </div><br />
</div></div>
imported>SeedBot