Formula:KLS:09.08:19: Difference between revisions

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<div id="alignleft"> << [[Formula:KLS:09.08:18|Formula:KLS:09.08:18]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:18|Formula:KLS:09.08:18]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:19|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:19|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Jacobi|Jacobi]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] >> </div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\lim_{N\rightarrow\infty}
\Ultra{\lambda}{2n}@{x}=\frac{\pochhammer{\lambda}{n}}{\pochhammer{\frac{1}{2}}{n}}
\Hahn{n}@{Nx}{\alpha}{\beta}{N}=\frac{\Jacobi{\alpha}{\beta}{n}@{1-2x}}{\Jacobi{\alpha}{\beta}{n}@{1}}
\Jacobi{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^2-1}
}</math></div>
}</math></div>


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


<span class="plainlinks">[http://dlmf.nist.gov/18.19#T1.t1.r3 <math>{\displaystyle Q_{n}}</math>]</span> : Hahn polynomial : [http://dlmf.nist.gov/18.19#T1.t1.r3 http://dlmf.nist.gov/18.19#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/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]
<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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<div id="alignleft"> << [[Formula:KLS:09.08:18|Formula:KLS:09.08:18]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:18|Formula:KLS:09.08:18]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:19|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:19|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Jacobi|Jacobi]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] >> </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 \Ultra{\lambda}{2n}@{x}=\frac{\pochhammer{\lambda}{n}}{\pochhammer{\frac{1}{2}}{n}} \Jacobi{\lambda-\frac{1}{2}}{-\frac{1}{2}}{n}@{2x^2-1} }}

Proof

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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 P^{(\alpha,\beta)}_{n}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.8 of KLS.

URL links

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