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Fungrim entry: 255d81

Π ⁣(n,ϕ,m)=Π ⁣(n,ϕ,m)\Pi\!\left(n, -\phi, m\right) = -\Pi\!\left(n, \phi, m\right)
Assumptions:nC  and  ϕC  and  mCn \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C}
\Pi\!\left(n, -\phi, m\right) = -\Pi\!\left(n, \phi, m\right)

n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C}
Fungrim symbol Notation Short description
IncompleteEllipticPiΠ ⁣(n,ϕ,m)\Pi\!\left(n, \phi, m\right) Legendre incomplete elliptic integral of the third kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(IncompleteEllipticPi(n, Neg(phi), m), Neg(IncompleteEllipticPi(n, phi, m)))),
    Variables(n, phi, m),
    Assumptions(And(Element(n, CC), Element(phi, CC), Element(m, CC))))

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2021-03-15 19:12:00.328586 UTC