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Fungrim entry: 398bb7

log ⁣(xy)=(xy)RC ⁣((x+y)24,xy)\log\!\left(\frac{x}{y}\right) = \left(x - y\right) R_C\!\left(\frac{{\left(x + y\right)}^{2}}{4}, x y\right)
Assumptions:y(0,)  and  x(0,)y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
\log\!\left(\frac{x}{y}\right) = \left(x - y\right) R_C\!\left(\frac{{\left(x + y\right)}^{2}}{4}, x y\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
Fungrim symbol Notation Short description
Loglog(z)\log(z) Natural logarithm
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Powab{a}^{b} Power
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(Log(Div(x, y)), Mul(Sub(x, y), CarlsonRC(Div(Pow(Add(x, y), 2), 4), Mul(x, y))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, 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