Formula:KLS:09.08:25: Difference between revisions

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<div id="drmf_head">
<div id="drmf_head">
<div id="alignleft"> << [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:25|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:25|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] >> </div>
</div>
</div>


<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\pseudoJacobi{n}@{x}{\nu}{N}=\frac{(-2\iunit)^nn!}{\pochhammer{n-2N-1}{n}}\Jacobi{-N-1+\iunit\nu}{-N-1-\iunit\nu}{n}@{\iunit x}
\Ultra{\lambda}{n}@{x}
=(2x)^{n} \frac{\pochhammer{\lambda}{n}}{n!}  
\HyperpFq{2}{1}@@{-\frac12 n,-\frac12 n+\frac12}{1-\lambda-n}{\frac1{x^2}}
}</math></div>
}</math></div>


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


<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi <math>{\displaystyle P_{n}}</math>]</span> : pseudo Jacobi polynomomal : [http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi]<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/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://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/16.2#E1 <math>{\displaystyle {{}_{p}F_{q}}}</math>]</span> : generalized hypergeometric function : [http://dlmf.nist.gov/16.2#E1 http://dlmf.nist.gov/16.2#E1]
<br />
<br />


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<br /><div id="drmf_foot">
<br /><div id="drmf_foot">
<div id="alignleft"> << [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:25|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:25|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] >> </div>
</div>
</div>

Latest revision as of 08:35, 22 December 2019


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Ultra{\lambda}{n}@{x} =(2x)^{n} \frac{\pochhammer{\lambda}{n}}{n!} \HyperpFq{2}{1}@@{-\frac12 n,-\frac12 n+\frac12}{1-\lambda-n}{\frac1{x^2}} }}

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}F_{q}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.8 of KLS.

URL links

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