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Fungrim entry: afabeb

F ⁣(πk2,m)=kK(m)F\!\left(\frac{\pi k}{2}, m\right) = k K(m)
Assumptions:mC  and  kZ  and  (k0  or  m1)m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)
F\!\left(\frac{\pi k}{2}, m\right) = k K(m)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)
Fungrim symbol Notation Short description
IncompleteEllipticFF ⁣(ϕ,m)F\!\left(\phi, m\right) Legendre incomplete elliptic integral of the first kind
Piπ\pi The constant pi (3.14...)
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(IncompleteEllipticF(Div(Mul(Pi, k), 2), m), Mul(k, EllipticK(m)))),
    Variables(m, k),
    Assumptions(And(Element(m, CC), Element(k, ZZ), Or(NotEqual(k, 0), NotEqual(m, 1)))))

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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