Formula:KLS:09.08:12: Difference between revisions

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<div id="drmf_head">
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<div id="alignleft"> << [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:12|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:12|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:13|Formula:KLS:09.08:13]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:13|Formula:KLS:09.08:13]] >> </div>
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<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\frac{2^{\alpha+\beta}}{R(1+R-t)^{\alpha}(1+R+t)^{\beta}}=
(1-2xt+t^2)^{-\lambda}=\sum_{n=0}^{\infty}\Ultra{\lambda}{n}@{x}t^n
\sum_{n=0}^{\infty}\Jacobi{\alpha}{\beta}{n}@{x}t^n
}</math></div>
}</math></div>
== Substitution(s) ==
<div align="left"><math>{\displaystyle R=\sqrt{1-2xt+t^2}}</math></div><br />


== Proof ==
== Proof ==
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<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:sum <math>{\displaystyle \Sigma}</math>]</span> : sum : [http://drmf.wmflabs.org/wiki/Definition:sum http://drmf.wmflabs.org/wiki/Definition:sum]<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:sum <math>{\displaystyle \Sigma}</math>]</span> : sum : [http://drmf.wmflabs.org/wiki/Definition:sum http://drmf.wmflabs.org/wiki/Definition:sum]<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/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">
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<div id="alignleft"> << [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:11|Formula:KLS:09.08:11]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:12|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:12|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:13|Formula:KLS:09.08:13]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:13|Formula:KLS:09.08:13]] >> </div>
</div>
</div>

Latest revision as of 07:35, 22 December 2019


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (1-2xt+t^2)^{-\lambda}=\sum_{n=0}^{\infty}\Ultra{\lambda}{n}@{x}t^n }}

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 \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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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