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Fungrim entry: 98688d

erf⁡(z)=2ze−z2π 1F1 ⁣(1,32,z2)\operatorname{erf}(z) = \frac{2 z {e}^{-{z}^{2}}}{\sqrt{\pi}} \,{}_1F_1\!\left(1, \frac{3}{2}, {z}^{2}\right)
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{erf}(z) = \frac{2 z {e}^{-{z}^{2}}}{\sqrt{\pi}} \,{}_1F_1\!\left(1, \frac{3}{2}, {z}^{2}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Erferf⁡(z)\operatorname{erf}(z) Error function
Expez{e}^{z} Exponential function
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Hypergeometric1F1 1F1 ⁣(a,b,z)\,{}_1F_1\!\left(a, b, z\right) Kummer confluent hypergeometric function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("98688d"),
    Formula(Equal(Erf(z), Mul(Div(Mul(Mul(2, z), Exp(Neg(Pow(z, 2)))), Sqrt(Pi)), Hypergeometric1F1(1, Div(3, 2), Pow(z, 2))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC