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Fungrim entry: 4f9844

sinc⁡(z)=∑n=0∞(−1)nz2n(2n+1)!\operatorname{sinc}(z) = \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n} {z}^{2 n}}{\left(2 n + 1\right)!}
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{sinc}(z) = \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n} {z}^{2 n}}{\left(2 n + 1\right)!}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sincsinc⁡(z)\operatorname{sinc}(z) Sinc function
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity∞\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("4f9844"),
    Formula(Equal(Sinc(z), Sum(Div(Mul(Pow(-1, n), Pow(z, Mul(2, n))), Factorial(Add(Mul(2, n), 1))), For(n, 0, Infinity)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC