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==Asymptotic==
<math>\begin{align}\log f(x)&=-\frac{\log^2x}{2 \log2}+\frac{\log x\cdot\log (-\log x)}{\log2}-\left(\frac{1}{2}frac12 +\frac{1+\log \log2}{\log2}\right)\log x -\frac{\log ^2(-\log x)}{2 \log 2log2 }+\frac{\log \log 2\cdot\log (-\log x)}{\log 2log2 }\\&+\left(\frac{6 \gamma ^2+12 \gamma_1-\pi ^2-6 \log ^2\log 2log2 }{12 \log 2}-\frac{7 \log 2}{12}-\frac{\log\pi}2\right)+O\!\left(\frac{\log^2(-\log x)}{2\log2\cdot \log x}- \right)frac{ \quadlog \textlog2\cdot\log(-\log x)} {for\log2\cdot\log x }+O \,!\left(\frac1{\log x} \to0^+,right)\quad \end{align}</math>
for <math>x\to0^+,</math> where <math>\gamma</math> is [[Euler's constant]], and <math>\gamma_1</math> is the [[Stieltjes constants|Stieltjes constant]].
==References==
