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Fungrim entry: 18f40c

sin ⁣(z)=eizeiz2i\sin\!\left(z\right) = \frac{{e}^{i z} - {e}^{-i z}}{2 i}
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(z\right) = \frac{{e}^{i z} - {e}^{-i z}}{2 i}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("18f40c"),
    Formula(Equal(Sin(z), Div(Sub(Exp(Mul(ConstI, z)), Exp(Mul(Neg(ConstI), z))), Mul(2, ConstI)))),
    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.

2019-08-25 15:30:03.056001 UTC