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Fungrim entry: 2aaba8

erf ⁣(z)=2π0zet2dt\operatorname{erf}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} {e}^{-{t}^{2}} \, dt
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{erf}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} {e}^{-{t}^{2}} \, dt

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Erferf ⁣(z)\operatorname{erf}\!\left(z\right) Error function
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
Integralabf ⁣(x)dx\int_{a}^{b} f\!\left(x\right) \, dx Integral
Expez{e}^{z} Exponential function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("2aaba8"),
    Formula(Equal(Erf(z), Mul(Div(2, Sqrt(ConstPi)), Integral(Exp(Neg(Pow(t, 2))), Tuple(t, 0, z))))),
    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.

2019-09-15 11:00:55.020619 UTC