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Fungrim entry: 36ef64

erfc ⁣(z)=2πzet2dt\operatorname{erfc}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} {e}^{-{t}^{2}} \, dt
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{erfc}\!\left(z\right) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} {e}^{-{t}^{2}} \, dt

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Erfcerfc ⁣(z)\operatorname{erfc}\!\left(z\right) Complementary 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
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("36ef64"),
    Formula(Equal(Erfc(z), Mul(Div(2, Sqrt(ConstPi)), Integral(Exp(Neg(Pow(t, 2))), Tuple(t, z, Infinity))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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2019-09-15 14:14:26.267625 UTC