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Fungrim entry: 9ccaef

Π ⁣(n,m)=RF ⁣(0,1m,1)+n3RJ ⁣(0,1m,1,1n)\Pi\!\left(n, m\right) = R_F\!\left(0, 1 - m, 1\right) + \frac{n}{3} R_J\!\left(0, 1 - m, 1, 1 - n\right)
Assumptions:nC  and  mC  and  m1n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \ne 1
TeX:
\Pi\!\left(n, m\right) = R_F\!\left(0, 1 - m, 1\right) + \frac{n}{3} R_J\!\left(0, 1 - m, 1, 1 - n\right)

n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \ne 1
Definitions:
Fungrim symbol Notation Short description
EllipticPiΠ ⁣(n,m)\Pi\!\left(n, m\right) Legendre complete elliptic integral of the third kind
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) Carlson symmetric elliptic integral of the third kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("9ccaef"),
    Formula(Equal(EllipticPi(n, m), Add(CarlsonRF(0, Sub(1, m), 1), Mul(Div(n, 3), CarlsonRJ(0, Sub(1, m), 1, Sub(1, n)))))),
    Variables(n, m),
    Assumptions(And(Element(n, CC), Element(m, CC), NotEqual(m, 1))))

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2021-03-15 19:12:00.328586 UTC