Formula:KLS:14.27:10
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x)=\frac{\gamma}{\sqrt{\cpi}}\exp@{-\gamma^2\ln^2@@{x}},\quad x>0,\quad\textrm{with}\quad \gamma^2=-\frac{1}{2\ln@@{q}} =\frac\gamma{\sqrt\cpi} x^{-\frac12}\exp@{-\gamma^2\ln^2@@{x}}, x>0 {\rm with} \gamma^2}}
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 \mathcal{D}_q^n}}
: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle S_{n}}}
: Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert
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{exp}}}
: exponential function : http://dlmf.nist.gov/4.2#E19
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{ln}}}
: principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
Bibliography
Equation in Section 14.27 of KLS.
URL links
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