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Fungrim entry: f35a37

E ⁣(ϕ,1)=(1)Re(ϕ)/π+1/2sin(ϕ)+2Re(ϕ)π+12E\!\left(\phi, 1\right) = {\left(-1\right)}^{\left\lfloor \operatorname{Re}(\phi) / \pi + 1 / 2 \right\rfloor} \sin(\phi) + 2 \left\lfloor \frac{\operatorname{Re}(\phi)}{\pi} + \frac{1}{2} \right\rfloor
Assumptions:ϕC\phi \in \mathbb{C}
E\!\left(\phi, 1\right) = {\left(-1\right)}^{\left\lfloor \operatorname{Re}(\phi) / \pi + 1 / 2 \right\rfloor} \sin(\phi) + 2 \left\lfloor \frac{\operatorname{Re}(\phi)}{\pi} + \frac{1}{2} \right\rfloor

\phi \in \mathbb{C}
Fungrim symbol Notation Short description
IncompleteEllipticEE ⁣(ϕ,m)E\!\left(\phi, m\right) Legendre incomplete elliptic integral of the second kind
Powab{a}^{b} Power
ReRe(z)\operatorname{Re}(z) Real part
Piπ\pi The constant pi (3.14...)
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(IncompleteEllipticE(phi, 1), Add(Mul(Pow(-1, Floor(Add(Div(Re(phi), Pi), Div(1, 2)))), Sin(phi)), Mul(2, Floor(Add(Div(Re(phi), Pi), Div(1, 2))))))),
    Assumptions(Element(phi, CC)))

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2021-03-15 19:12:00.328586 UTC