-
artanh u ±
artanh v =
artanh ( u ± v 1 ± u v ) {\displaystyle \operatorname {
artanh} u\pm \operatorname {
artanh} v=\operatorname {
artanh} \left({\frac...
- 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 ( 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}...
-
denoted "cosh−1", "acosh" or
sometimes "arccosh") area
hyperbolic tangent "
artanh" (also
denoted "tanh−1", "atanh" or
sometimes "arctanh") area hyperbolic...
- 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...
-
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...
- u 0 γ 0 + α T c ) −
artanh ( u 0 c ) } u ( τ ) = c tanh {
artanh ( u 0 c ) + α τ c } X ( τ ) = X 0 + c 2 α { cosh [
artanh ( u 0 c ) + α τ c...
- ) = 2
artanh r {\displaystyle \ln \left({\frac {1+r}{1-r}}\right)=2\operatorname {
artanh} r}
where artanh {\displaystyle \operatorname {
artanh} } is...
- 1 a
artanh 1 − 1 a 2 x 2 + C {\displaystyle \int \operatorname {arccsc}(ax)\,dx=x\operatorname {arccsc}(ax)+{\frac {1}{a}}\,\operatorname {
artanh} \,{\sqrt...
