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Fungrim entry: 24c17b

sinc(z)=n=1cos ⁣(z2n)\operatorname{sinc}(z) = \prod_{n=1}^{\infty} \cos\!\left(\frac{z}{{2}^{n}}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{sinc}(z) = \prod_{n=1}^{\infty} \cos\!\left(\frac{z}{{2}^{n}}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Productnf(n)\prod_{n} f(n) Product
Coscos(z)\cos(z) Cosine
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("24c17b"),
    Formula(Equal(Sinc(z), Product(Cos(Div(z, Pow(2, n))), For(n, 1, Infinity)))),
    Variables(z),
    Assumptions(Element(z, CC)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC