Fungrim entry: 11687b

\sin(z) = z \prod_{k=1}^{\infty} \left(1 - \frac{{z}^{2}}{{\pi}^{2} {k}^{2}}\right)

Assumptions:

z \in \mathbb{C}

TeX:

\sin(z) = z \prod_{k=1}^{\infty} \left(1 - \frac{{z}^{2}}{{\pi}^{2} {k}^{2}}\right)

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin(z)$	Sine
`Product`	$\prod_{n} f(n)$	Product
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("11687b"),
    Formula(Equal(Sin(z), Mul(z, Product(Parentheses(Sub(1, Div(Pow(z, 2), Mul(Pow(Pi, 2), Pow(k, 2))))), For(k, 1, 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