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Fungrim entry: b1d132

sinc ⁣(az)=12aaaeizxdx\operatorname{sinc}\!\left(a z\right) = \frac{1}{2 a} \int_{-a}^{a} {e}^{i z x} \, dx
Assumptions:zC  and  aC  and  a0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0
TeX:
\operatorname{sinc}\!\left(a z\right) = \frac{1}{2 a} \int_{-a}^{a} {e}^{i z x} \, dx

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0
Definitions:
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:
Entry(ID("b1d132"),
    Formula(Equal(Sinc(Mul(a, z)), Mul(Div(1, Mul(2, a)), Integral(Exp(Mul(Mul(ConstI, z), x)), For(x, Neg(a), a))))),
    Variables(a, z),
    Assumptions(And(Element(z, CC), Element(a, CC), NotEqual(a, 0))))

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2020-08-27 09:56:25.682319 UTC