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Fungrim entry: abadc7

erf ⁣(z)=2zπ1F1 ⁣(12,32,z2)\operatorname{erf}\!\left(z\right) = \frac{2 z}{\sqrt{\pi}} \,{}_1F_1\!\left(\frac{1}{2}, \frac{3}{2}, -{z}^{2}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{erf}\!\left(z\right) = \frac{2 z}{\sqrt{\pi}} \,{}_1F_1\!\left(\frac{1}{2}, \frac{3}{2}, -{z}^{2}\right)

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...)
Hypergeometric1F11F1 ⁣(a,b,z)\,{}_1F_1\!\left(a, b, z\right) Kummer confluent hypergeometric function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("abadc7"),
    Formula(Equal(Erf(z), Mul(Div(Mul(2, z), Sqrt(ConstPi)), Hypergeometric1F1(Div(1, 2), Div(3, 2), 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.

2019-09-15 11:00:55.020619 UTC