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Fungrim entry: a6667d

sin(r+2)(z)=sin(r)(z){\sin}^{(r + 2)}(z) = -{\sin}^{(r)}(z)
Assumptions:zCandrZ0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}
TeX:
{\sin}^{(r + 2)}(z) = -{\sin}^{(r)}(z)

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
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("a6667d"),
    Formula(Equal(ComplexDerivative(Sin(z), For(z, z, Add(r, 2))), Neg(ComplexDerivative(Sin(z), For(z, z, r))))),
    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