Fungrim entry: f340cb

\sin(z) = \sum_{k=0}^{\infty} {\left(-1\right)}^{k} \frac{{z}^{2 k + 1}}{\left(2 k + 1\right)!}

Assumptions:

z \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
`Sin`	$\sin(z)$	Sine
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	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

Sine

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

2021-03-15 19:12:00.328586 UTC