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Fungrim entry: de0638

RC ⁣(−x,−y)=−iRC ⁣(x,y)R_C\!\left(-x, -y\right) = -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)
TeX:
R_C\!\left(-x, -y\right) = -i R_C\!\left(x, y\right)

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
ConstIii Imaginary unit
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("de0638"),
    Formula(Equal(CarlsonRC(Neg(x), Neg(y)), Neg(Mul(ConstI, CarlsonRC(x, y))))),
    Variables(x, y),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)))))

Topics using this entry

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