Formula:KLS:09.08:11: Difference between revisions
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<div id="alignleft"> << [[Formula:KLS:09.08:10|Formula:KLS:09.08:10]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:10|Formula:KLS:09.08:10]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:11|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:11|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08:12|Formula:KLS:09.08:12]] >> </div> | <div id="alignright"> [[Formula:KLS:09.08:12|Formula:KLS:09.08:12]] >> </div> | ||
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<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
(1-x)^{\ | (1-x^2)^{\lambda-\frac{1}{2}}\Ultra{\lambda}{n}@{x}= | ||
\frac{(-1)^n}{2^nn!}\left(\frac{d}{dx}\right)^n | \frac{\pochhammer{2\lambda}{n}(-1)^n}{\pochhammer{\lambda+\frac{1}{2}}{n}2^nn!}\left(\frac{d}{dx}\right)^n | ||
\left[(1-x)^{n | \left[(1-x^2)^{\lambda+n-\frac{1}{2}}\right] | ||
}</math></div> | }</math></div> | ||
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== Symbols List == | == Symbols List == | ||
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1. | <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 /> | <br /> | ||
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<div id="alignleft"> << [[Formula:KLS:09.08:10|Formula:KLS:09.08:10]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:10|Formula:KLS:09.08:10]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:11|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:11|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08:12|Formula:KLS:09.08:12]] >> </div> | <div id="alignright"> [[Formula:KLS:09.08:12|Formula:KLS:09.08:12]] >> </div> | ||
</div> | </div> | ||
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 (1-x^2)^{\lambda-\frac{1}{2}}\Ultra{\lambda}{n}@{x}= \frac{\pochhammer{2\lambda}{n}(-1)^n}{\pochhammer{\lambda+\frac{1}{2}}{n}2^nn!}\left(\frac{d}{dx}\right)^n \left[(1-x^2)^{\lambda+n-\frac{1}{2}}\right] }}
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
Bibliography
Equation in Section 9.8 of KLS.
URL links
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