Formula:KLS:09.08:21: Difference between revisions
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<div id="alignleft"> << [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:21|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:21|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08: | <div id="alignright"> [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] >> </div> | ||
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<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
\ | \frac{h_n}{h_0}= | ||
\frac | \frac\lambda{\lambda+n} \frac{\pochhammer{2\lambda}{n}}{n!} | ||
h_0 | |||
}</math></div> | }</math></div> | ||
== Substitution(s) == | |||
<div align="left"><math>{\displaystyle \frac{h_n}{h_0} | |||
=\frac{\cpi^\frac12 \EulerGamma@{\lambda+\frac12}}{\EulerGamma@{\lambda+1}} | |||
\frac{h_n}{h_0 (\Ultra{\lambda}{n}@{1})^2} | |||
= | |||
\frac\lambda{\lambda+n} \frac{n!}{\pochhammer{2\lambda}{n}}}</math></div><br /> | |||
== Proof == | == Proof == | ||
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== Symbols List == | == Symbols List == | ||
<span class="plainlinks">[http://dlmf.nist.gov/ | <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. | <span class="plainlinks">[http://dlmf.nist.gov/5.19.E4 <math>{\displaystyle \pi}</math>]</span> : ratio of a circle's circumference to its diameter : [http://dlmf.nist.gov/5.19.E4 http://dlmf.nist.gov/5.19.E4]<br /> | ||
<span class="plainlinks">[http://dlmf.nist.gov/5.2#E1 <math>{\displaystyle \Gamma}</math>]</span> : Euler's gamma function : [http://dlmf.nist.gov/5.2#E1 http://dlmf.nist.gov/5.2#E1]<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 /> | <br /> | ||
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<div id="alignleft"> << [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] </div> | <div id="alignleft"> << [[Formula:KLS:09.08:20|Formula:KLS:09.08:20]] </div> | ||
<div id="aligncenter"> [[Jacobi#KLS:09.08:21|formula in Jacobi]] </div> | <div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:21|formula in Jacobi: Special cases]] </div> | ||
<div id="alignright"> [[Formula:KLS:09.08: | <div id="alignright"> [[Formula:KLS:09.08:24|Formula:KLS:09.08:24]] >> </div> | ||
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Revision as of 23:34, 5 March 2017
Substitution(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 (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 \pi}}
: ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Gamma}}
: Euler's gamma function : http://dlmf.nist.gov/5.2#E1
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.