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Fungrim entry: b1d132

sinc⁡ ⁣(az)=12a∫−aaeizx dx\operatorname{sinc}\!\left(a z\right) = \frac{1}{2 a} \int_{-a}^{a} {e}^{i z x} \, 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}{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
Integral∫abf(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))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC