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Fungrim entry: 2f6818

zeroszC[sin ⁣(z)]={πn:nZ}\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[\sin\!\left(z\right)\right] = \left\{ \pi n : n \in \mathbb{Z} \right\}
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[\sin\!\left(z\right)\right] = \left\{ \pi n : n \in \mathbb{Z} \right\}
Definitions:
Fungrim symbol Notation Short description
ZeroszerosP(x)f ⁣(x)\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right) Zeros (roots) of function
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ConstPiπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("2f6818"),
    Formula(Equal(Zeros(Brackets(Sin(z)), z, Element(z, CC)), SetBuilder(Mul(ConstPi, n), n, Element(n, ZZ)))))

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

2019-08-25 15:30:03.056001 UTC