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Definition:qLaguerre - Revision history
2024-03-29T11:32:52Z
Revision history for this page on the wiki
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Move page script: Move page script moved page Definition:qLaguerre to D:qLaguerre
2019-12-22T06:50:28Z
<p>Move page script moved page <a href="/wiki/Definition:qLaguerre" title="Definition:qLaguerre">Definition:qLaguerre</a> to <a href="https://www.wikidata.org/wiki/qLaguerre" class="extiw" title="d:qLaguerre">D:qLaguerre</a></p>
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imported>SeedBot: DRMF
2017-03-05T22:33:13Z
<p>DRMF</p>
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imported>SeedBot
https://drmf-beta.wmflabs.org/index.php?title=Definition:qLaguerre&diff=477&oldid=prev
imported>SeedBot: DRMF
2017-03-05T22:32:22Z
<p>DRMF</p>
<p><b>New page</b></p><div><div id="drmf_head"><br />
<div id="alignleft"> << [[Definition:qtmqKrawtchouk|Definition:qtmqKrawtchouk]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:ctsqHermite|Definition:ctsqHermite]] >> </div><br />
</div><br />
<br />
The LaTeX DLMF and DRMF macro '''\qLaguerre''' represents the <math>q</math>-Laguerre polynomial.<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 />
:'''\qLaguerre{n}''' produces <math>{\displaystyle \qLaguerre{n}}</math><br /><br />
:'''\qLaguerre[\alpha]{n}''' produces <math>{\displaystyle \qLaguerre[\alpha]{n}}</math><br /><br />
:'''\qLaguerre{n}@{x}{q}''' produces <math>{\displaystyle \qLaguerre{n}@{x}{q}}</math><br /><br />
:'''\qLaguerre[\alpha]{n}@{x}{q}''' produces <math>{\displaystyle \qLaguerre[\alpha]{n}@{x}{q}}</math><br /><br />
:'''\qLaguerre{n}@@{x}{q}''' produces <math>{\displaystyle \qLaguerre{n}@@{x}{q}}</math><br /><br />
:'''\qLaguerre[\alpha]{n}@@{x}{q}''' produces <math>{\displaystyle \qLaguerre[\alpha]{n}@@{x}{q}}</math><br /><br />
<br />
These are defined by<br />
<math>{\displaystyle<br />
\qLaguerre[\alpha]{n}@{x}{q}:=\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n}}\,<br />
\qHyperrphis{1}{1}@@{q^{-n}}{q^{\alpha+1}}{q}{-q^{n+\alpha+1}x}<br />
}</math><br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:qLaguerre <math>{\displaystyle L_n^{(\alpha)}}</math>]</span> : <math>{\displaystyle q}</math>-Laguerre polynomial : [http://drmf.wmflabs.org/wiki/Definition:qLaguerre http://drmf.wmflabs.org/wiki/Definition:qLaguerre]<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 />
<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 /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Definition:qtmqKrawtchouk|Definition:qtmqKrawtchouk]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:ctsqHermite|Definition:ctsqHermite]] >> </div><br />
</div></div>
imported>SeedBot