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Fungrim entry: c28288

E ⁣(ϕ+kπ,m)=E ⁣(ϕ,m)+2kE(m)E\!\left(\phi + k \pi, m\right) = E\!\left(\phi, m\right) + 2 k E(m)
Assumptions:ϕC  and  mC  and  kZ\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
TeX:
E\!\left(\phi + k \pi, m\right) = E\!\left(\phi, m\right) + 2 k E(m)

\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
Definitions:
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:
Entry(ID("c28288"),
    Formula(Equal(IncompleteEllipticE(Add(phi, Mul(k, Pi)), m), Add(IncompleteEllipticE(phi, m), Mul(Mul(2, k), EllipticE(m))))),
    Variables(phi, m, k),
    Assumptions(And(Element(phi, CC), Element(m, CC), Element(k, ZZ))))

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2021-03-15 19:12:00.328586 UTC