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Definition:qExpKLS - Revision history
2024-03-28T18:16:22Z
Revision history for this page on the wiki
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Move page script: Move page script moved page Definition:qExpKLS to D:qExpKLS
2019-12-22T06:49:55Z
<p>Move page script moved page <a href="/wiki/Definition:qExpKLS" title="Definition:qExpKLS">Definition:qExpKLS</a> to <a href="https://www.wikidata.org/wiki/qExpKLS" class="extiw" title="d:qExpKLS">D:qExpKLS</a></p>
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imported>SeedBot: DRMF
2017-03-05T22:33:12Z
<p>DRMF</p>
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imported>SeedBot
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imported>SeedBot: DRMF
2017-03-05T22:32:21Z
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imported>SeedBot
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imported>SeedBot: DRMF
2017-03-05T22:30:30Z
<p>DRMF</p>
<p><b>New page</b></p><div><div id="drmf_head"><br />
<div id="alignleft"> << [[Definition:qHyperrWs|Definition:qHyperrWs]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qexpKLS|Definition:qexpKLS]] >> </div><br />
</div><br />
<br />
The LaTeX DLMF and DRMF macro '''\qExpKLS''' represents a <math>q</math>-analogue of the <br />
<math>\exp</math> function: <math>\qExpKLS{q}</math>.<br />
<br />
This macro is in the category of real or complex valued functions.<br />
<br />
In math mode, this macro can be called in the following ways:<br />
<br />
:'''\qExpKLS{q}''' produces <math>{\displaystyle \qExpKLS{q}}</math><br /><br />
:'''\qExpKLS{q}@{z}''' produces <math>{\displaystyle \qExpKLS{q}@{z}}</math><br /><br />
:'''\qExpKLS{q}@@{z}''' produces <math>{\displaystyle \qExpKLS{q}@@{z}}</math><br /><br />
<br />
These are defined by<br />
<math>{\displaystyle<br />
\qExpKLS{q}@{z}:=\qHyperrphis{0}{0}@@{-}{-}{q}{-z}:=<br />
\sum_{n=0}^{\infty}\frac{q^{\binom{n}{2}}}{\qPochhammer{q}{q}{n}}z^n=\qPochhammer{-z}{q}{\infty},\quad 0<|q|<1.<br />
}</math><br />
<br />
== Symbols List ==<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://dlmf.nist.gov/4.2#E19 <math>{\displaystyle \mathrm{exp}}</math>]</span> : exponential function : [http://dlmf.nist.gov/4.2#E19 http://dlmf.nist.gov/4.2#E19]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/17.4#E1 <math>{\displaystyle {{}_{r}\phi_{s}}}</math>]</span> : basic hypergeometric (or <math>{\displaystyle q}</math>-hypergeometric) function : [http://dlmf.nist.gov/17.4#E1 http://dlmf.nist.gov/17.4#E1]<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/1.2#E1 <math>{\displaystyle \binom{n}{k}}</math>]</span> : binomial coefficient : [http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/1.2#E1] [http://dlmf.nist.gov/26.3#SS1.p1 http://dlmf.nist.gov/26.3#SS1.p1]<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:qHyperrWs|Definition:qHyperrWs]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qexpKLS|Definition:qexpKLS]] >> </div><br />
</div></div>
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