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Fungrim entry: f64eef

sinc ⁣(πz)=n=1(1z2n2)\operatorname{sinc}\!\left(\pi z\right) = \prod_{n=1}^{\infty} \left(1 - \frac{{z}^{2}}{{n}^{2}}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{sinc}\!\left(\pi z\right) = \prod_{n=1}^{\infty} \left(1 - \frac{{z}^{2}}{{n}^{2}}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Piπ\pi The constant pi (3.14...)
Productnf(n)\prod_{n} f(n) Product
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f64eef"),
    Formula(Equal(Sinc(Mul(Pi, z)), Product(Parentheses(Sub(1, Div(Pow(z, 2), Pow(n, 2)))), 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