Formula:KLS:09.08:10: Difference between revisions

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<div id="alignleft"> << [[Formula:KLS:09.08:09|Formula:KLS:09.08:09]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:09|Formula:KLS:09.08:09]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:10|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:10|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] >> </div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\frac{d}{dx}\left[(1-x)^\alpha(1+x)^\beta \Jacobi{\alpha}{\beta}{n}@{x}\right]
\frac{d}{dx}\left[(1-x^2)^{\lambda-\textstyle\frac{1}{2}}\Ultra{\lambda}{n}@{x}\right]
{}=-2(n+1)(1-x)^{\alpha-1}(1+x)^{\beta-1}\Jacobi{\alpha-1}{\beta-1}{n+1}@{x}
{}=-\frac{(n+1)(2\lambda+n-1)}{2(\lambda-1)}(1-x^2)^{\lambda-\textstyle\frac{3}{2}}\Ultra{\lambda-1}{n+1}@{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]
<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 />
<br />


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<div id="alignleft"> << [[Formula:KLS:09.08:09|Formula:KLS:09.08:09]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:09|Formula:KLS:09.08:09]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:10|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:10|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] >> </div>
</div>
</div>

Revision as of 23:34, 5 March 2017


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{d}{dx}\left[(1-x^2)^{\lambda-\textstyle\frac{1}{2}}\Ultra{\lambda}{n}@{x}\right] {}=-\frac{(n+1)(2\lambda+n-1)}{2(\lambda-1)}(1-x^2)^{\lambda-\textstyle\frac{3}{2}}\Ultra{\lambda-1}{n+1}@{x} }}

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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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