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Fungrim entry: 81f7db

F ⁣(π2,m)=K(m)F\!\left(\frac{-\pi}{2}, m\right) = -K(m)
Assumptions:mCm \in \mathbb{C}
F\!\left(\frac{-\pi}{2}, m\right) = -K(m)

m \in \mathbb{C}
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
Source code for this entry:
    Formula(Equal(IncompleteEllipticF(Div(Neg(Pi), 2), m), Neg(EllipticK(m)))),
    Assumptions(Element(m, CC)))

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2021-03-15 19:12:00.328586 UTC