Formula:KLS:09.08:01: Difference between revisions
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{{DISPLAYTITLE:Formula:KLS:09.08:01}} | {{DISPLAYTITLE:Formula:KLS:09.08:01}} | ||
<div id="drmf_head"> | <div id="drmf_head"> | ||
<div id="alignleft"> << [[ | <div id="alignleft"> << [[:30|:30]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:01|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:01|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[ | <div id="alignright"> [[Jacobi:_Special_cases|Jacobi: Special cases]] >> </div> | ||
</div> | </div> | ||
<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
\ | \Ultra{\lambda}{n}@{x}=\frac{\pochhammer{2\lambda}{n}}{\pochhammer{\lambda+\frac{1}{2}}{n}} | ||
\ | \Jacobi{\lambda-\frac{1}{2}}{\lambda-\frac{1}{2}}{n}@{x} | ||
}</math></div> | }</math></div> | ||
== Constraint(s) == | |||
<div align="left"><math>{\displaystyle \lambda\neq 0}</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 /> | ||
<span class="plainlinks">[http://dlmf.nist.gov/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii] | <span class="plainlinks">[http://dlmf.nist.gov/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii]<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] | |||
<br /> | <br /> | ||
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<br /><div id="drmf_foot"> | <br /><div id="drmf_foot"> | ||
<div id="alignleft"> << [[ | <div id="alignleft"> << [[:30|:30]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:01|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:01|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[ | <div id="alignright"> [[Jacobi:_Special_cases|Jacobi: Special cases]] >> </div> | ||
</div> | </div> | ||
Latest revision as of 08:34, 22 December 2019
Constraint(s)
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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a)_n}}
: Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
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
We ask users to provide relevant URL links in this space.