Fungrim entry: 5c9675

\int_{0}^{\pi / 4} \frac{1}{\operatorname{sinc}^{2}\!\left(x\right)} \, dx = \frac{\pi \log(2)}{4} + G - \frac{{\pi}^{2}}{16}

TeX:

\int_{0}^{\pi / 4} \frac{1}{\operatorname{sinc}^{2}\!\left(x\right)} \, dx = \frac{\pi \log(2)}{4} + G - \frac{{\pi}^{2}}{16}

Definitions:

Fungrim symbol	Notation	Short description
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Pow`	${a}^{b}$	Power
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Pi`	$\pi$	The constant pi (3.14...)
`Log`	$\log(z)$	Natural logarithm
`ConstCatalan`	$G$	Catalan's constant

Source code for this entry:

Entry(ID("5c9675"),
    Formula(Equal(Integral(Div(1, Pow(Sinc(x), 2)), For(x, 0, Div(Pi, 4))), Sub(Add(Div(Mul(Pi, Log(2)), 4), ConstCatalan), Div(Pow(Pi, 2), 16)))))

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