Fungrim home page

Fungrim entry: 11687b

sin ⁣(z)=zk=1(1z2π2k2)\sin\!\left(z\right) = z \prod_{k=1}^{\infty} \left(1 - \frac{{z}^{2}}{{\pi}^{2} {k}^{2}}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(z\right) = 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
Sinsin ⁣(z)\sin\!\left(z\right) Sine
Productnf ⁣(n)\prod_{n} f\!\left(n\right) Product
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
Infinity\infty Positive infinity
CCC\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(ConstPi, 2), Pow(k, 2))))), Tuple(k, 1, 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.

2019-08-21 11:44:15.926409 UTC