# Fungrim entry: 98688d

$\operatorname{erf}(z) = \frac{2 z {e}^{-{z}^{2}}}{\sqrt{\pi}} \,{}_1F_1\!\left(1, \frac{3}{2}, {z}^{2}\right)$
Assumptions:$z \in \mathbb{C}$
TeX:
\operatorname{erf}(z) = \frac{2 z {e}^{-{z}^{2}}}{\sqrt{\pi}} \,{}_1F_1\!\left(1, \frac{3}{2}, {z}^{2}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Erf$\operatorname{erf}(z)$ Error function
Exp${e}^{z}$ Exponential function
Pow${a}^{b}$ Power
Sqrt$\sqrt{z}$ Principal square root
Pi$\pi$ The constant pi (3.14...)
Hypergeometric1F1$\,{}_1F_1\!\left(a, b, z\right)$ Kummer confluent hypergeometric function
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("98688d"),
Formula(Equal(Erf(z), Mul(Div(Mul(Mul(2, z), Exp(Neg(Pow(z, 2)))), Sqrt(Pi)), Hypergeometric1F1(1, Div(3, 2), Pow(z, 2))))),
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.

2021-03-15 19:12:00.328586 UTC