Fungrim entry: 45f05f

$\frac{1}{\operatorname{sinc}\!\left(\frac{\pi}{z}\right)} = \int_{0}^{\infty} \frac{1}{{x}^{z} + 1} \, dx$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 1$
TeX:
\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
Definitions:
Fungrim symbol Notation Short description
Sinc$\operatorname{sinc}(z)$ Sinc function
Pi$\pi$ The constant pi (3.14...)
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("45f05f"),
Formula(Equal(Div(1, Sinc(Div(Pi, z))), Integral(Div(1, Add(Pow(x, z), 1)), For(x, 0, Infinity)))),
Variables(z),
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