Fungrim entry: 36ef64

\operatorname{erfc}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} {e}^{-{t}^{2}} \, dt

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{erfc}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} {e}^{-{t}^{2}} \, dt

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Erfc`	$\operatorname{erfc}\!\left(z\right)$	Complementary error function
`Sqrt`	$\sqrt{z}$	Principal square root
`ConstPi`	$\pi$	The constant pi (3.14...)
`Exp`	${e}^{z}$	Exponential function
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("36ef64"),
    Formula(Equal(Erfc(z), Mul(Div(2, Sqrt(ConstPi)), Integral(Exp(Neg(Pow(t, 2))), Tuple(t, z, Infinity))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Error functions

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

2019-06-18 07:49:59.356594 UTC