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Fungrim entry: 99ad29

sinc ⁣(πz)=1/21/2e2πizxdx\operatorname{sinc}\!\left(\pi z\right) = \int_{-1 / 2}^{1 / 2} {e}^{2 \pi i z x} \, dx
Assumptions:zCz \in \mathbb{C}
\operatorname{sinc}\!\left(\pi z\right) = \int_{-1 / 2}^{1 / 2} {e}^{2 \pi i z x} \, dx

z \in \mathbb{C}
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
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Sinc(Mul(Pi, z)), Integral(Exp(Mul(Mul(Mul(Mul(2, Pi), ConstI), z), x)), For(x, Neg(Div(1, 2)), Div(1, 2))))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC