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Fungrim entry: 36ef64

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

z \in \mathbb{C}
Fungrim symbol Notation Short description
Erfcerfc(z)\operatorname{erfc}(z) Complementary error function
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Integralabf(x)dx\int_{a}^{b} f(x) \, 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:
    Formula(Equal(Erfc(z), Mul(Div(2, Sqrt(Pi)), Integral(Exp(Neg(Pow(t, 2))), For(t, z, Infinity))))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC