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Formula:KLS:09.04:18 - Revision history
2024-03-28T11:46:25Z
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imported>SeedBot: DRMF
2017-03-05T22:34:07Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:KLS:09.04:18}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:KLS:09.04:16|Formula:KLS:09.04:16]] </div><br />
<div id="aligncenter"> [[Continuous_Hahn#KLS:09.04:18|formula in Continuous Hahn]] </div><br />
<div id="alignright"> [[Formula:KLS:09.04:19|Formula:KLS:09.04:19]] >> </div><br />
</div><br />
<br />
<br /><div align="center"><math>{\displaystyle <br />
\omega(x;a,b,c,d)\ctsHahn{n}@{x}{a}{b}{c}{d}<br />
{}=\frac{(-1)^n}{n!}\left(\frac{\delta}{\delta x}\right)^n<br />
\left[\omega(x;a+\textstyle\frac{1}{2}n,b+\textstyle\frac{1}{2}n<br />
c+\textstyle\frac{1}{2}n,d+\textstyle\frac{1}{2}n)\right]<br />
}</math></div><br />
<br />
== Substitution(s) ==<br />
<br />
<div align="left"><math>{\displaystyle \omega(x;a,b,c,d)=\EulerGamma@{a+\iunit x}\EulerGamma@{b+\iunit x}\EulerGamma@{c-\iunit x}\EulerGamma@{d-\iunit x}}</math></div><br /><br />
<br />
== 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://dlmf.nist.gov/18.19#P2.p1 <math>{\displaystyle p_{n}}</math>]</span> : continuous Hahn polynomial : [http://dlmf.nist.gov/18.19#P2.p1 http://dlmf.nist.gov/18.19#P2.p1]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/5.2#E1 <math>{\displaystyle \Gamma}</math>]</span> : Euler's gamma function : [http://dlmf.nist.gov/5.2#E1 http://dlmf.nist.gov/5.2#E1]<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 /><br />
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== Bibliography==<br />
<br />
<span class="plainlinks">[http://homepage.tudelft.nl/11r49/askey/contents.html Equation in Section 9.4]</span> of [[Bibliography#KLS|'''KLS''']].<br />
<br />
== 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:09.04:16|Formula:KLS:09.04:16]] </div><br />
<div id="aligncenter"> [[Continuous_Hahn#KLS:09.04:18|formula in Continuous Hahn]] </div><br />
<div id="alignright"> [[Formula:KLS:09.04:19|Formula:KLS:09.04:19]] >> </div><br />
</div></div>
imported>SeedBot