Formula:KLS:09.08:06: Difference between revisions

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m Move page script moved page Formula:KLS:09.08:06 to F:KLS:09.08:06
 
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<div id="drmf_head">
<div id="drmf_head">
<div id="alignleft"> << [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:06|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:06|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:07|Formula:KLS:09.08:07]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:07|Formula:KLS:09.08:07]] >> </div>
</div>
</div>


<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\Jacobi{\alpha}{\beta}{n}@{x}=\frac{\pochhammer{n+\alpha+\beta+1}{n}}{2^nn!}\monicJacobi{\alpha}{\beta}{n}@@{x}{x}
\Ultra{\lambda}{n}@{x}=\frac{2^n\pochhammer{\lambda}{n}}{n!}\monicUltra{\lambda}{n}@@{x}{x}
}</math></div>
}</math></div>


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


<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 />
<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/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii]<br />
<span class="plainlinks">[http://dlmf.nist.gov/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii]<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:monicJacobi <math>{\displaystyle {\widehat P}^{(\alpha,\beta)}_{n}}</math>]</span> : monic Jacobi polynomial : [http://drmf.wmflabs.org/wiki/Definition:monicJacobi http://drmf.wmflabs.org/wiki/Definition:monicJacobi]
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:monicUltra <math>{\displaystyle {\widehat C}^{\mu}_{n}}</math>]</span> : monic ultraspherical/Gegenbauer polynomial : [http://drmf.wmflabs.org/wiki/Definition:monicUltra http://drmf.wmflabs.org/wiki/Definition:monicUltra]
<br />
<br />


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<br /><div id="drmf_foot">
<br /><div id="drmf_foot">
<div id="alignleft"> << [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:06|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:06|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:07|Formula:KLS:09.08:07]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:07|Formula:KLS:09.08:07]] >> </div>
</div>
</div>

Latest revision as of 08:34, 22 December 2019


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Ultra{\lambda}{n}@{x}=\frac{2^n\pochhammer{\lambda}{n}}{n!}\monicUltra{\lambda}{n}@@{x}{x} }}

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 (a)_n}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {\widehat C}^{\mu}_{n}}}  : monic ultraspherical/Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:monicUltra

Bibliography

Equation in Section 9.8 of KLS.

URL links

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