Fungrim entry: 4a5b9a

\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
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstCatalan`	$G$	Catalan's constant
`RiemannZeta`	$\zeta\!\left(s\right)$	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)))))

Topics using this entry

Sinc function

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

2021-03-15 19:12:00.328586 UTC