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Fungrim entry: 087a7c

F ⁣(asin ⁣(1m),m)=K ⁣(1m)mF\!\left(\operatorname{asin}\!\left(\frac{1}{\sqrt{m}}\right), m\right) = \frac{K\!\left(\frac{1}{m}\right)}{\sqrt{m}}
Assumptions:mC{0}m \in \mathbb{C} \setminus \left\{0\right\}
F\!\left(\operatorname{asin}\!\left(\frac{1}{\sqrt{m}}\right), m\right) = \frac{K\!\left(\frac{1}{m}\right)}{\sqrt{m}}

m \in \mathbb{C} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
IncompleteEllipticFF ⁣(ϕ,m)F\!\left(\phi, m\right) Legendre incomplete elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
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(Asin(Div(1, Sqrt(m))), m), Div(EllipticK(Div(1, m)), Sqrt(m)))),
    Assumptions(Element(m, SetMinus(CC, Set(0)))))

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2021-03-15 19:12:00.328586 UTC