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Fungrim entry: 23e0a7

RF ⁣(x,y,z)=iRF ⁣(x,y,z)R_F\!\left(-x, -y, z\right) = \overline{i R_F\!\left(x, y, -z\right)}
Assumptions:x[0,)  and  y[0,)  and  z[0,)x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
R_F\!\left(-x, -y, z\right) = \overline{i R_F\!\left(x, y, -z\right)}

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
Fungrim symbol Notation Short description
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
Conjugatez\overline{z} Complex conjugate
ConstIii Imaginary unit
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(CarlsonRF(Neg(x), Neg(y), z), Conjugate(Mul(ConstI, CarlsonRF(x, y, Neg(z)))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

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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