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Fungrim entry: 4becdd

RC ⁣(x,y)=iRC ⁣(x,y)R_C\!\left(-x, y\right) = \overline{i R_C\!\left(x, -y\right)}
Assumptions:x(0,)  and  y(0,)x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
R_C\!\left(-x, y\right) = \overline{i R_C\!\left(x, -y\right)}

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