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Fungrim entry: f340cb

sin(z)=k=0(1)kz2k+1(2k+1)!\sin(z) = \sum_{k=0}^{\infty} {\left(-1\right)}^{k} \frac{{z}^{2 k + 1}}{\left(2 k + 1\right)!}
Assumptions:zCz \in \mathbb{C}
TeX:
\sin(z) = \sum_{k=0}^{\infty} {\left(-1\right)}^{k} \frac{{z}^{2 k + 1}}{\left(2 k + 1\right)!}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f340cb"),
    Formula(Equal(Sin(z), Sum(Mul(Pow(-1, k), Div(Pow(z, Add(Mul(2, k), 1)), Factorial(Add(Mul(2, k), 1)))), For(k, 0, Infinity)))),
    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.

2019-10-05 13:11:19.856591 UTC