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Fungrim entry: 729c78

sinc ⁣(πz)=01cos ⁣(πzx)dx\operatorname{sinc}\!\left(\pi z\right) = \int_{0}^{1} \cos\!\left(\pi z x\right) \, dx
Assumptions:zCz \in \mathbb{C}
\operatorname{sinc}\!\left(\pi z\right) = \int_{0}^{1} \cos\!\left(\pi z x\right) \, 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
Coscos(z)\cos(z) Cosine
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Sinc(Mul(Pi, z)), Integral(Cos(Mul(Mul(Pi, z), x)), For(x, 0, 1)))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC