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Fungrim entry: 4a5b9a

0π/2xsinc(x)dx=2πG7ζ ⁣(3)2\int_{0}^{\pi / 2} \frac{x}{\operatorname{sinc}(x)} \, dx = 2 \pi G - \frac{7 \zeta\!\left(3\right)}{2}
TeX:
\int_{0}^{\pi / 2} \frac{x}{\operatorname{sinc}(x)} \, dx = 2 \pi G - \frac{7 \zeta\!\left(3\right)}{2}
Definitions:
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Piπ\pi The constant pi (3.14...)
ConstCatalanGG Catalan's constant
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Source code for this entry:
Entry(ID("4a5b9a"),
    Formula(Equal(Integral(Div(x, Sinc(x)), For(x, 0, Div(Pi, 2))), Sub(Mul(Mul(2, Pi), ConstCatalan), Div(Mul(7, RiemannZeta(3)), 2)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC