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Fungrim entry: 6a8889

sin⁡ ⁣(z+2πk)=sin⁡ ⁣(z)\sin\!\left(z + 2 \pi k\right) = \sin\!\left(z\right)
Assumptions:z∈C and⁡ k∈Zz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}
TeX:
\sin\!\left(z + 2 \pi k\right) = \sin\!\left(z\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Sinsin⁡ ⁣(z)\sin\!\left(z\right) Sine
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("6a8889"),
    Formula(Equal(Sin(Add(z, Mul(Mul(2, ConstPi), k))), Sin(z))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZ))))

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

2019-06-18 07:49:59.356594 UTC