Gold 7

Logarithmic integral function

Gold ID

7

Link

https://sigir21.wmflabs.org/wiki/Logarithmic_integral_function#math.57.2

Formula

$\mathrm{li}(x)=\underset{\epsilon \to 0+}{\lim }(\underset{0}{\overset{1-\epsilon }{\int }}\frac{dt}{\ln t}+\underset{1+\epsilon }{\overset{x}{\int }}\frac{dt}{\ln t})$

TeX Source

\operatorname{li}(x) = \lim_{\varepsilon \to 0+} \left( \int_0^{1-\varepsilon} \frac{dt}{\ln t} + \int_{1+\varepsilon}^x \frac{dt}{\ln t} \right)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\logint@{x} = \lim_{\varepsilon \to 0+}(\int_0^{1-\varepsilon} \frac{\diff{t}}{\ln t} + \int_{1+\varepsilon}^x \frac{\diff{t}}{\ln t})

Expected (Gold Entry)

\logint@{x} = \lim_{\varepsilon \to 0+}(\int_0^{1-\varepsilon} \frac{\diff{t}}{\ln t} + \int_{1+\varepsilon}^x \frac{\diff{t}}{\ln t})

Mathematica

Translation

LogIntegral[x] == Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \[CurlyEpsilon], x}, GenerateConditions->None], \[CurlyEpsilon] -> 0, Direction -> "FromAbove", GenerateConditions->None]

Expected (Gold Entry)

LogIntegral[x] == Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \[CurlyEpsilon]}]+ Integrate[Divide[1,Log[t]], {t, 1 + \[CurlyEpsilon], x}], \[CurlyEpsilon] -> 0, Direction -> "FromAbove"]

Maple

Translation

Li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)

Expected (Gold Entry)

Li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)