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Fungrim entry: e2c10d

sinc⁡ ⁣(az)=1a∫0acos⁡ ⁣(zx) dx\operatorname{sinc}\!\left(a z\right) = \frac{1}{a} \int_{0}^{a} \cos\!\left(z x\right) \, dx
Assumptions:z∈C  and⁡  a∈C  and⁡  a≠0z \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}{a} \int_{0}^{a} \cos\!\left(z x\right) \, 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
Integral∫abf(x) dx\int_{a}^{b} f(x) \, dx Integral
Coscos⁡(z)\cos(z) Cosine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e2c10d"),
    Formula(Equal(Sinc(Mul(a, z)), Mul(Div(1, a), Integral(Cos(Mul(z, x)), For(x, 0, a))))),
    Variables(a, z),
    Assumptions(And(Element(z, CC), Element(a, CC), NotEqual(a, 0))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC