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Definition:qMeixnerPollaczek - Revision history
2024-03-29T12:51:09Z
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2019-12-22T06:50:26Z
<p>Move page script moved page <a href="/wiki/Definition:qMeixnerPollaczek" title="Definition:qMeixnerPollaczek">Definition:qMeixnerPollaczek</a> to <a href="https://www.wikidata.org/wiki/qMeixnerPollaczek" class="extiw" title="d:qMeixnerPollaczek">D:qMeixnerPollaczek</a></p>
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imported>SeedBot: DRMF
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<p>DRMF</p>
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imported>SeedBot
https://drmf-beta.wmflabs.org/index.php?title=Definition:qMeixnerPollaczek&diff=473&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:monicAffqKrawtchouk|Definition:monicAffqKrawtchouk]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qtmqKrawtchouk|Definition:qtmqKrawtchouk]] >> </div><br />
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<br />
The LaTeX DLMF and DRMF macro '''\qMeixnerPollaczek''' represents the <math>q</math>-Meixner Pollaczek 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 />
:'''\qMeixnerPollaczek{n}''' produces <math>{\displaystyle \qMeixnerPollaczek{n}}</math><br /><br />
:'''\qMeixnerPollaczek{n}@{x}{a}{q}''' produces <math>{\displaystyle \qMeixnerPollaczek{n}@{x}{a}{q}}</math><br /><br />
<br />
These are defined by<br />
<math>{\displaystyle<br />
\qMeixnerPollaczek{n}@{x}{a}{q}:=a^{-n}\expe^{-in\phi}\frac{\qPochhammer{a^2}{q}{n}}{\qPochhammer{q}{q}{n}}\,<br />
\qHyperrphis{3}{2}@@{q^{-n},a\expe^{i(\theta+2\phi)},a\expe^{-i\theta}}{a^2,0}{q}{q}<br />
}</math><br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek <math>{\displaystyle P_{n}}</math>]</span> : <math>{\displaystyle q}</math>-Meixner-Pollaczek polynomial : [http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek]<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/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:monicAffqKrawtchouk|Definition:monicAffqKrawtchouk]] </div><br />
<div id="aligncenter"> [[Main_Page|Main Page]] </div><br />
<div id="alignright"> [[Definition:qtmqKrawtchouk|Definition:qtmqKrawtchouk]] >> </div><br />
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imported>SeedBot