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Fungrim entry: 612b21

sin(r)(z)=sin ⁣(z+πr2){\sin}^{(r)}(z) = \sin\!\left(z + \frac{\pi r}{2}\right)
Assumptions:zCandrZ0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}
TeX:
{\sin}^{(r)}(z) = \sin\!\left(z + \frac{\pi r}{2}\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sinsin(z)\sin(z) Sine
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("612b21"),
    Formula(Equal(ComplexDerivative(Sin(z), For(z, z, r)), Sin(Add(z, Div(Mul(ConstPi, r), 2))))),
    Variables(z, r),
    Assumptions(And(Element(z, CC), Element(r, ZZGreaterEqual(0)))))

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

2019-10-05 13:11:19.856591 UTC