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Fungrim entry: 08583a

sinc(z)=1211eizxdx\operatorname{sinc}(z) = \frac{1}{2} \int_{-1}^{1} {e}^{i z x} \, dx
Assumptions:zCz \in \mathbb{C}
\operatorname{sinc}(z) = \frac{1}{2} \int_{-1}^{1} {e}^{i z x} \, dx

z \in \mathbb{C}
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
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(z), Mul(Div(1, 2), Integral(Exp(Mul(Mul(ConstI, z), x)), For(x, -1, 1))))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC