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Fungrim entry: b5bd5d

erf(z)=2πez2\operatorname{erf}'(z) = \frac{2}{\sqrt{\pi}} {e}^{-{z}^{2}}
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{erf}'(z) = \frac{2}{\sqrt{\pi}} {e}^{-{z}^{2}}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Erferf(z)\operatorname{erf}(z) Error function
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Expez{e}^{z} Exponential function
Powab{a}^{b} Power
CCC\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

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