-
artanh u ±
artanh v =
artanh ( u ± v 1 ± u v ) {\displaystyle \operatorname {
artanh} u\pm \operatorname {
artanh} v=\operatorname {
artanh} \left({\frac...
- coordinates.
Using the
inverse hyperbolic function artanh, the
rapidity w
corresponding to
velocity v is w =
artanh(v/c)
where c is the
speed of light. For low...
-
denoted "cosh−1", "acosh" or
sometimes "arccosh")
inverse hyperbolic tangent "
artanh" (also
denoted "tanh−1", "atanh" or
sometimes "arctanh")
inverse hyperbolic...
- of a
Pearson correlation coefficient is its
inverse hyperbolic tangent (
artanh). When the
sample correlation coefficient r is near 1 or -1, its distribution...
-
artanh ( ρ ) ∈ [
artanh ( r ) ± z α / 2 SE ] {\displaystyle 100(1-\alpha )\%{\text{CI}}:\operatorname {
artanh} (\rho )\in [\operatorname {
artanh}...
- \mathrm {d} y=} = ∫ 0 1 [ 2 y
artanh ( y ) − 2 y
artanh ( 1 − x 2 y 1 − x 2 y 2 ) ] x = 0 x = 1 d y = ∫ 0 1 2 y
artanh ( y ) d y = {\displaystyle...
-
artanh ( a x ) d x = x
artanh ( a x ) + ln ( 1 − a 2 x 2 ) 2 a + C {\displaystyle \int \operatorname {
artanh} (ax)\,dx=x\operatorname {
artanh}...
- ) = 2
artanh r {\displaystyle \ln \left({\frac {1+r}{1-r}}\right)=2\operatorname {
artanh} r}
where artanh {\displaystyle \operatorname {
artanh} } is...
-
artanh ( tanh ( y a ) cosh ( x a ) ) {\displaystyle \operatorname {
artanh} \left(\tanh(y_{a})\cosh(x_{a})\right)} . To the y-axis it is
artanh ...
- g}\ln {\frac {1+\alpha v}{1-\alpha v}}={\frac {\mathrm {
artanh} (\alpha v)}{\alpha g}},} with
artanh the
inverse hyperbolic tangent function. Alternatively...
