Formula:KLS:14.19:12: Difference between revisions
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Latest revision as of 07:38, 22 December 2019
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle y(x)=\ctsqLaguerre{\alpha}{n}@{x}{q}}}
&
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x):=w(x;q^{\alpha}|q) =\left|\frac{\qPochhammer{\expe^{2\iunit\theta}}{q}{\infty}} {\qPochhammer{q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{\iunit\theta} q^{\frac{1}{2}\alpha+\frac{3}{4}}\expe^{\iunit\theta}}{q}{\infty}}\right|^2 =\left|\frac{\qPochhammer{\expe^{\iunit\theta},-\expe^{\iunit\theta}}{q^{\frac{1}{2}}}{\infty}} {\qPochhammer{q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{\iunit\theta}}{q^{\frac{1}{2}}}{\infty}}\right|^2 =\frac{h(x,1)h(x,-1)h(x,q^{\frac{1}{2}})h(x,-q^{\frac{1}{2}})} {h(x,q^{\frac{1}{2}\alpha+\frac{1}{4}})h(x,q^{\frac{1}{2}\alpha+\frac{3}{4}})}}}
&
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle h(x,\alpha):=\prod_{k=0}^{\infty}\left(1-2\alpha xq^k+\alpha^2q^{2k}\right) =\qPochhammer{\alpha\expe^{\iunit\theta},\alpha\expe^{-\iunit\theta}}{q}{\infty}}}
&
Proof
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Symbols List
& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(n)}_{\alpha}}}
: continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}
: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}
: the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}
: imaginary unit : http://dlmf.nist.gov/1.9.i
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Pi}}
: product : http://drmf.wmflabs.org/wiki/Definition:prod
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{cos}}}
: cosine function : http://dlmf.nist.gov/4.14#E2
Bibliography
Equation in Section 14.19 of KLS.
URL links
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