Formula:KLS:09.08:05: Difference between revisions

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<div id="alignleft"> << [[Formula:KLS:09.08:04|Formula:KLS:09.08:04]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:04|Formula:KLS:09.08:04]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:05|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:05|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] >> </div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
x\monicJacobi{\alpha}{\beta}{n}@@{x}{x}=\monicJacobi{\alpha}{\beta}{n+1}@@{x}{x}+\frac{\beta^2-\alpha^2}{(2n+\alpha+\beta)(2n+\alpha+\beta+2)}\monicJacobi{\alpha}{\beta}{n}@@{x}{x}
x\monicUltra{\lambda}{n}@@{x}{x}=\monicUltra{\lambda}{n+1}@@{x}{x}+\frac{n(n+2\lambda-1)}{4(n+\lambda-1)(n+\lambda)}\monicUltra{\lambda}{n-1}@@{x}{x}
{}+\frac{4n(n+\alpha)(n+\beta)(n+\alpha+\beta)}
{(2n+\alpha+\beta-1)(2n+\alpha+\beta)^2(2n+\alpha+\beta+1)}\monicJacobi{\alpha}{\beta}{n-1}@@{x}{x}
}</math></div>
}</math></div>
== Constraint(s) ==
<div align="left"><math>{\displaystyle \;\;}</math></div><br />


== Proof ==
== Proof ==
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== Symbols List ==
== Symbols List ==


<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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<div id="alignleft"> << [[Formula:KLS:09.08:04|Formula:KLS:09.08:04]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:04|Formula:KLS:09.08:04]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:05|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:05|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] >> </div>
</div>
</div>

Revision as of 00:34, 6 March 2017


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

 : 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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