Formula:KLS:09.08:18: Difference between revisions

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<div id="alignleft"> << [[Formula:KLS:09.08:17|Formula:KLS:09.08:17]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:17|Formula:KLS:09.08:17]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:18|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:18|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:19|Formula:KLS:09.08:19]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:19|Formula:KLS:09.08:19]] >> </div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\lim_{t\rightarrow\infty}
\lim_{\alpha\rightarrow\infty}
\frac{\ctsHahn{n}@{\frac{1}{2}xt}{\frac{1}{2}(\alpha+1-\iunit t)}{\frac{1}{2}(\beta+1+\iunit t)}{
\alpha^{-\frac{1}{2}n}\Ultra{\alpha+\frac{1}{2}}{n}@{\alpha^{-\frac{1}{2}}x}=\frac{\Hermite{n}@{x}}{n!}
\frac{1}{2}(\alpha+1+\iunit t)}{\frac{1}{2}(\beta+1-\iunit t})}{t^n}=\Jacobi{\alpha}{\beta}{n}@{x}
}</math></div>
}</math></div>


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== Symbols List ==
== Symbols List ==


<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 />
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r5 <math>{\displaystyle C^{\mu}_{n}}</math>]</span> : ultraspherical/Gegenbauer polynomial : [http://dlmf.nist.gov/18.3#T1.t1.r5 http://dlmf.nist.gov/18.3#T1.t1.r5]<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 />
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r28 <math>{\displaystyle H_{n}}</math>]</span> : Hermite polynomial <math>{\displaystyle H_n}</math> : [http://dlmf.nist.gov/18.3#T1.t1.r28 http://dlmf.nist.gov/18.3#T1.t1.r28]
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r3 <math>{\displaystyle P^{(\alpha,\beta)}_{n}}</math>]</span> : Jacobi polynomial : [http://dlmf.nist.gov/18.3#T1.t1.r3 http://dlmf.nist.gov/18.3#T1.t1.r3]
<br />
<br />


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<br /><div id="drmf_foot">
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<div id="alignleft"> << [[Formula:KLS:09.08:17|Formula:KLS:09.08:17]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:17|Formula:KLS:09.08:17]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:18|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:18|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:19|Formula:KLS:09.08:19]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:19|Formula:KLS:09.08:19]] >> </div>
</div>
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Revision as of 00:34, 6 March 2017


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lim_{\alpha\rightarrow\infty} \alpha^{-\frac{1}{2}n}\Ultra{\alpha+\frac{1}{2}}{n}@{\alpha^{-\frac{1}{2}}x}=\frac{\Hermite{n}@{x}}{n!} }}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C^{\mu}_{n}}}  : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle H_{n}}}  : Hermite polynomial Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle H_n}}  : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.8 of KLS.

URL links

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