Formula:KLS:09.08:07: Difference between revisions
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<div id="alignleft"> << [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:07|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:07|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08:08|Formula:KLS:09.08:08]] >> </div> | <div id="alignright"> [[Formula:KLS:09.08:08|Formula:KLS:09.08:08]] >> </div> | ||
</div> | </div> | ||
<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
(1-x^2)y''(x) | (1-x^2)y''(x)-(2\lambda+1)xy'(x)+n(n+2\lambda)y(x)=0 | ||
}</math></div> | }</math></div> | ||
== Substitution(s) == | == Substitution(s) == | ||
<div align="left"><math>{\displaystyle y(x)=\ | <div align="left"><math>{\displaystyle y(x)=\Ultra{\lambda}{n}@{x}}</math></div><br /> | ||
== Proof == | == Proof == | ||
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== Symbols List == | == Symbols List == | ||
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1. | <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:09.08:06|Formula:KLS:09.08:06]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:06|Formula:KLS:09.08:06]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:07|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:07|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08:08|Formula:KLS:09.08:08]] >> </div> | <div id="alignright"> [[Formula:KLS:09.08:08|Formula:KLS:09.08:08]] >> </div> | ||
</div> | </div> | ||
Latest revision as of 07:34, 22 December 2019
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (1-x^2)y''(x)-(2\lambda+1)xy'(x)+n(n+2\lambda)y(x)=0 }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle y(x)=\Ultra{\lambda}{n}@{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
We ask users to provide relevant URL links in this space.