Fungrim home page

Fungrim entry: 45f05f

1sinc ⁣(πz)=01xz+1dx\frac{1}{\operatorname{sinc}\!\left(\frac{\pi}{z}\right)} = \int_{0}^{\infty} \frac{1}{{x}^{z} + 1} \, dx
Assumptions:zC  and  Re(z)>1z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 1
\frac{1}{\operatorname{sinc}\!\left(\frac{\pi}{z}\right)} = \int_{0}^{\infty} \frac{1}{{x}^{z} + 1} \, dx

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 1
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Piπ\pi The constant pi (3.14...)
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    Formula(Equal(Div(1, Sinc(Div(Pi, z))), Integral(Div(1, Add(Pow(x, z), 1)), For(x, 0, Infinity)))),
    Assumptions(And(Element(z, CC), Greater(Re(z), 1))))

Topics using this entry

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