Formula:KLS:09.08:04: Difference between revisions

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<div id="drmf_head">
<div id="drmf_head">
<div id="alignleft"> << [[Formula:KLS:09.08:03|Formula:KLS:09.08:03]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:03|Formula:KLS:09.08:03]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:04|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:04|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] >> </div>
</div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
x\Jacobi{\alpha}{\beta}{n}@{x}=\frac{2(n+1)(n+\alpha+\beta+1)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)}\Jacobi{\alpha}{\beta}{n+1}@{x}
2(n+\lambda)x\Ultra{\lambda}{n}@{x}=(n+1)\Ultra{\lambda}{n+1}@{x}+(n+2\lambda-1)\Ultra{\lambda}{n-1}@{x}
{}+\frac{\beta^2-\alpha^2}{(2n+\alpha+\beta)(2n+\alpha+\beta+2)}\Jacobi{\alpha}{\beta}{n}@{x}
{}+\frac{2(n+\alpha)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)}\Jacobi{\alpha}{\beta}{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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<br /><div id="drmf_foot">
<br /><div id="drmf_foot">
<div id="alignleft"> << [[Formula:KLS:09.08:03|Formula:KLS:09.08:03]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:03|Formula:KLS:09.08:03]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:04|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:04|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:05|Formula:KLS:09.08:05]] >> </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 2(n+\lambda)x\Ultra{\lambda}{n}@{x}=(n+1)\Ultra{\lambda}{n+1}@{x}+(n+2\lambda-1)\Ultra{\lambda}{n-1}@{x} }}

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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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