https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Q-Racah_polynomials 2026-04-10T04:32:46Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Q-Racah_polynomials&diff=22981&oldid=prev 2011-09-05T07:43:31Z

<p>Various citation cleanup (identifiers mostly) using <a href="/index.php?title=Testwiki:AWB&amp;action=edit&amp;redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a></p> <p><b>New page</b></p><div>{{DISPLAYTITLE:&#039;&#039;q&#039;&#039;-Charlier polynomials }}<br /> In mathematics, the &#039;&#039;&#039;&#039;&#039;q&#039;&#039;-Charlier polynomials&#039;&#039;&#039; are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]]. {{harvs|txt | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010|loc=14}} give a detailed list of their properties.<br /> <br /> ==Definition==<br /> <br /> The &#039;&#039;&#039;q-Charlier polynomials&#039;&#039;&#039; are given in terms of the [[basic hypergeometric function]] by<br /> :&lt;math&gt;\displaystyle c_n(x;a;q) = {}_2\phi_1(q^{-n},x;0;q,-q^{n+1}/a)&lt;/math&gt;<br /> <br /> ==Orthogonality==<br /> {{Empty section|date=September 2011}}<br /> <br /> ==Recurrence and difference relations==<br /> {{Empty section|date=September 2011}}<br /> <br /> ==Rodrigues formula==<br /> {{Empty section|date=September 2011}}<br /> <br /> ==Generating function==<br /> {{Empty section|date=September 2011}}<br /> <br /> ==Relation to other polynomials==<br /> {{Empty section|date=September 2011}}<br /> <br /> ==References==<br /> <br /> *{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=[[Cambridge University Press]] | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 | mr=2128719 | year=2004 | volume=96}}<br /> *{{Citation | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}}<br /> *{{dlmf|id=18|title=|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}<br /> <br /> [[Category:Orthogonal polynomials]]<br /> [[Category:Q-analogs]]<br /> [[Category:Special hypergeometric functions]]</div>

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