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Fungrim entry: 12765e

atan ⁣(z)=i2log ⁣(1+iz1iz)\operatorname{atan}\!\left(z\right) = -\frac{i}{2} \log\!\left(\frac{1 + i z}{1 - i z}\right)
Assumptions:zCandzi[1,)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z i \notin \left[1, \infty\right)
TeX:
\operatorname{atan}\!\left(z\right) = -\frac{i}{2} \log\!\left(\frac{1 + i z}{1 - i z}\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z i \notin \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
ConstIii Imaginary unit
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("12765e"),
    Formula(Equal(Atan(z), Mul(Neg(Div(ConstI, 2)), Log(Div(Add(1, Mul(ConstI, z)), Sub(1, Mul(ConstI, z))))))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(Mul(z, ConstI), ClosedOpenInterval(1, Infinity)))))

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2019-09-19 20:12:49.583742 UTC