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imported>SeedBot: DRMF
2017-03-05T22:34:38Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:KLS:01.14:05}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:KLS:01.14:04|Formula:KLS:01.14:04]] </div><br />
<div id="aligncenter"> [[Some_q-analogues_of_special_functions#KLS:01.14:05|formula in Some q-analogues of special functions]] </div><br />
<div id="alignright"> [[Formula:KLS:01.14:06|Formula:KLS:01.14:06]] >> </div><br />
</div><br />
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<br /><div align="center"><math>{\displaystyle <br />
\qcosKLS{q}@{z}:=\frac{\qexpKLS{q}@{\iunit z)+{\mathrm e}_q(-\iunit z}}{2}=<br />
\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n}}{\qPochhammer{q}{q}{2n}}<br />
}</math></div><br />
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== 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://drmf.wmflabs.org/wiki/Definition:qcosKLS <math>{\displaystyle \mathrm{cos}_{q}}</math>]</span> : <math>{\displaystyle q}</math>-analogue of the cosine function <math>{\displaystyle \cos_q}</math> used in KLS : [http://drmf.wmflabs.org/wiki/Definition:qcosKLS http://drmf.wmflabs.org/wiki/Definition:qcosKLS]<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 exponential function <math>{\displaystyle \mathrm{e}_{q}}</math> used in KLS : [http://drmf.wmflabs.org/wiki/Definition:qexpKLS http://drmf.wmflabs.org/wiki/Definition:qexpKLS]<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/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 />
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== Bibliography==<br />
<br />
<span class="plainlinks">[http://homepage.tudelft.nl/11r49/askey/contents.html Equation in Section 1.14]</span> of [[Bibliography#KLS|'''KLS''']].<br />
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== 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:KLS:01.14:04|Formula:KLS:01.14:04]] </div><br />
<div id="aligncenter"> [[Some_q-analogues_of_special_functions#KLS:01.14:05|formula in Some q-analogues of special functions]] </div><br />
<div id="alignright"> [[Formula:KLS:01.14:06|Formula:KLS:01.14:06]] >> </div><br />
</div></div>
imported>SeedBot