# Fungrim entry: cb93ea

$\operatorname{erf}(z) = \frac{z}{\sqrt{{z}^{2}}} - \frac{{e}^{-{z}^{2}}}{z \sqrt{\pi}} U^{*}\!\left(\frac{1}{2}, \frac{1}{2}, {z}^{2}\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0$
TeX:
\operatorname{erf}(z) = \frac{z}{\sqrt{{z}^{2}}} - \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}}\; z \ne 0
Definitions:
Fungrim symbol Notation Short description
Erf$\operatorname{erf}(z)$ Error function
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
HypergeometricUStar$U^{*}\!\left(a, b, z\right)$ Scaled Tricomi confluent hypergeometric function
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("cb93ea"),
Formula(Equal(Erf(z), Sub(Div(z, Sqrt(Pow(z, 2))), 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), NotEqual(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.

2021-03-15 19:12:00.328586 UTC