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Fungrim entry: 622772

erfi⁡ ⁣(z)=2π∫0zet2 dt\operatorname{erfi}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} {e}^{{t}^{2}} \, dt
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{erfi}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} {e}^{{t}^{2}} \, dt

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Erfierfi⁡ ⁣(z)\operatorname{erfi}\!\left(z\right) Imaginary error function
Sqrtz\sqrt{z} Principal square root
ConstPiπ\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("622772"),
    Formula(Equal(Erfi(z), Mul(Div(2, Sqrt(ConstPi)), Integral(Exp(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.

2019-06-18 07:49:59.356594 UTC