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Fungrim entry: 2b7b1d

zsinc(x)dx=π2Si(z)\int_{z}^{\infty} \operatorname{sinc}(x) \, dx = \frac{\pi}{2} - \operatorname{Si}(z)
Assumptions:zCz \in \mathbb{C}
TeX:
\int_{z}^{\infty} \operatorname{sinc}(x) \, dx = \frac{\pi}{2} - \operatorname{Si}(z)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Infinity\infty Positive infinity
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("2b7b1d"),
    Formula(Equal(Integral(Sinc(x), For(x, z, Infinity)), Sub(Div(Pi, 2), SinIntegral(z)))),
    Variables(z),
    Assumptions(Element(z, CC)))

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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