Fungrim home page

Fungrim entry: 2cdd2f

atanh⁡ ⁣(xy)=xRC ⁣(y2,y2−x2)\operatorname{atanh}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2}, {y}^{2} - {x}^{2}\right)
Assumptions:y∈(0,∞)  and⁡  x∈(−y,y)y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(-y, y\right)
TeX:
\operatorname{atanh}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2}, {y}^{2} - {x}^{2}\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(-y, y\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
Powab{a}^{b} Power
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("2cdd2f"),
    Formula(Equal(Atanh(Div(x, y)), Mul(x, CarlsonRC(Pow(y, 2), Sub(Pow(y, 2), Pow(x, 2)))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, OpenInterval(Neg(y), y)))))

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