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Fungrim entry: 75e141

E ⁣(ϕ,1)=sin(ϕ)E\!\left(\phi, 1\right) = \sin(\phi)
Assumptions:ϕC  and  (Re(ϕ)[π2,π2)  or  ϕ=π2)\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(\operatorname{Re}(\phi) \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right) \;\mathbin{\operatorname{or}}\; \phi = \frac{\pi}{2}\right)
E\!\left(\phi, 1\right) = \sin(\phi)

\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(\operatorname{Re}(\phi) \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right) \;\mathbin{\operatorname{or}}\; \phi = \frac{\pi}{2}\right)
Fungrim symbol Notation Short description
IncompleteEllipticEE ⁣(ϕ,m)E\!\left(\phi, m\right) Legendre incomplete elliptic integral of the second kind
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Piπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(IncompleteEllipticE(phi, 1), Sin(phi))),
    Assumptions(And(Element(phi, CC), Or(Element(Re(phi), ClosedOpenInterval(Div(Neg(Pi), 2), Div(Pi, 2))), Equal(phi, Div(Pi, 2))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC