# 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...)
Integral$\int_{a}^{b} f\!\left(x\right) \, dx$ Integral
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

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

2019-09-15 14:14:26.267625 UTC