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Fungrim entry: 8ef3d7

zsinc(x)dx=Si(z)+π2\int_{-\infty}^{z} \operatorname{sinc}(x) \, dx = \operatorname{Si}(z) + \frac{\pi}{2}
Assumptions:zCz \in \mathbb{C}
TeX:
\int_{-\infty}^{z} \operatorname{sinc}(x) \, dx = \operatorname{Si}(z) + \frac{\pi}{2}

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("8ef3d7"),
    Formula(Equal(Integral(Sinc(x), For(x, Neg(Infinity), z)), Add(SinIntegral(z), Div(Pi, 2)))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2020-08-27 09:56:25.682319 UTC