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Fungrim entry: a14442

E ⁣(πk2,m)=kE(m)E\!\left(\frac{\pi k}{2}, m\right) = k E(m)
Assumptions:mC  and  kZm \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
E\!\left(\frac{\pi k}{2}, m\right) = k E(m)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
Fungrim symbol Notation Short description
IncompleteEllipticEE ⁣(ϕ,m)E\!\left(\phi, m\right) Legendre incomplete elliptic integral of the second kind
Piπ\pi The constant pi (3.14...)
EllipticEE(m)E(m) Legendre complete elliptic integral of the second kind
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(IncompleteEllipticE(Div(Mul(Pi, k), 2), m), Mul(k, EllipticE(m)))),
    Variables(m, k),
    Assumptions(And(Element(m, CC), Element(k, ZZ))))

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2021-03-15 19:12:00.328586 UTC