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Fungrim entry: d6703a

G=7ζ ⁣(3)4π+2π01(atan(x))2xdxG = \frac{7 \zeta\!\left(3\right)}{4 \pi} + \frac{2}{\pi} \int_{0}^{1} \frac{{\left(\operatorname{atan}(x)\right)}^{2}}{x} \, dx
G = \frac{7 \zeta\!\left(3\right)}{4 \pi} + \frac{2}{\pi} \int_{0}^{1} \frac{{\left(\operatorname{atan}(x)\right)}^{2}}{x} \, dx
Fungrim symbol Notation Short description
ConstCatalanGG Catalan's constant
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Piπ\pi The constant pi (3.14...)
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Source code for this entry:
    Formula(Equal(ConstCatalan, Add(Div(Mul(7, RiemannZeta(3)), Mul(4, Pi)), Mul(Div(2, Pi), Integral(Div(Pow(Atan(x), 2), x), For(x, 0, 1)))))))

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2021-03-15 19:12:00.328586 UTC