# Fungrim entry: ae3110

$\operatorname{erfc}(z) = \frac{{e}^{-{z}^{2}}}{z \sqrt{\pi}} U^{*}\!\left(\frac{1}{2}, \frac{1}{2}, {z}^{2}\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(z) > 0$
TeX:
\operatorname{erfc}(z) = \frac{{e}^{-{z}^{2}}}{z \sqrt{\pi}} U^{*}\!\left(\frac{1}{2}, \frac{1}{2}, {z}^{2}\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(z) > 0
Definitions:
Fungrim symbol Notation Short description
Erfc$\operatorname{erfc}(z)$ Complementary error function
Exp${e}^{z}$ Exponential function
Pow${a}^{b}$ Power
Sqrt$\sqrt{z}$ Principal square root
Pi$\pi$ The constant pi (3.14...)
HypergeometricUStar$U^{*}\!\left(a, b, z\right)$ Scaled Tricomi confluent hypergeometric function
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("ae3110"),
Formula(Equal(Erfc(z), Mul(Div(Exp(Neg(Pow(z, 2))), Mul(z, Sqrt(Pi))), HypergeometricUStar(Div(1, 2), Div(1, 2), Pow(z, 2))))),
Variables(z),
Assumptions(And(Element(z, CC), Greater(Re(z), 0))))

## Topics using this entry

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

2019-12-30 15:00:46.909060 UTC