Formula:KLS:09.08:27: Difference between revisions
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<div id="alignleft"> << [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:27|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:27|formula in Jacobi: Special cases]] </div> | ||
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<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
\Ultra{\lambda}{ | \frac{\Ultra{\lambda}{n}@{x}}{\Ultra{\lambda}{n}@{1}}= | ||
\frac{\Jacobi{\lambda-\frac12}{\lambda-\frac12}{n}@{x}}{\Jacobi{\lambda-\frac12}{\lambda-\frac12}{n}@{1}} ,\qquad | |||
\Ultra{\lambda}{n}@{x} | |||
}</math></div> | }</math></div> | ||
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<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/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/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.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] | ||
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<div id="alignleft"> << [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:26|Formula:KLS:09.08:26]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:27|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:27|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[: | <div id="alignright"> [[Formula:KLS:09.08:28|Formula:KLS:09.08:28]] >> </div> | ||
</div> | </div> | ||
Latest revision as of 08:35, 22 December 2019
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{\Ultra{\lambda}{n}@{x}}{\Ultra{\lambda}{n}@{1}}= \frac{\Jacobi{\lambda-\frac12}{\lambda-\frac12}{n}@{x}}{\Jacobi{\lambda-\frac12}{\lambda-\frac12}{n}@{1}} ,\qquad \Ultra{\lambda}{n}@{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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(\alpha,\beta)}_{n}}}
: Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
Bibliography
Equation in Section 9.8 of KLS.
URL links
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