Fungrim entry: b5bd5d

\operatorname{erf}'(z) = \frac{2}{\sqrt{\pi}} {e}^{-{z}^{2}}

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{erf}'(z) = \frac{2}{\sqrt{\pi}} {e}^{-{z}^{2}}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`Erf`	$\operatorname{erf}(z)$	Error function
`Sqrt`	$\sqrt{z}$	Principal square root
`Pi`	$\pi$	The constant pi (3.14...)
`Exp`	${e}^{z}$	Exponential function
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("b5bd5d"),
    Formula(Equal(ComplexDerivative(Erf(z), For(z, z, 1)), Mul(Div(2, Sqrt(Pi)), Exp(Neg(Pow(z, 2)))))),
    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.

2021-03-15 19:12:00.328586 UTC