-
angle measure, for
example arsinh ( sinh a ) = a {\displaystyle \operatorname {
arsinh} (\sinh a)=a} and sinh (
arsinh x ) = x . {\displaystyle...
- functions. The
inverse hyperbolic functions are:
inverse hyperbolic sine "
arsinh" (also
denoted "sinh−1", "asinh" or
sometimes "arcsinh")
inverse hyperbolic...
- gd − 1 φ =
arsinh ( tan φ ) , {\displaystyle \operatorname {gd} ^{-1}\varphi =\operatorname {
arsinh} (\tan \varphi ),} and
arsinh {\displaystyle...
- α e − δ x − θ
arsinh ( x ) , {\displaystyle P(x)={\frac {M}{1+\alpha e^{-\delta x-\theta \operatorname {
arsinh} (x)}}},}
where arsinh {\displaystyle...
- here. ∫
arsinh ( a x ) d x = x
arsinh ( a x ) − a 2 x 2 + 1 a + C {\displaystyle \int \operatorname {
arsinh} (ax)\,dx=x\operatorname {
arsinh} (ax)-{\frac...
- {1-V^{2}/c^{2}}}}
Phase 3 : c / a
arsinh ( a T a / c ) {\displaystyle :\quad c/a\ {\text{
arsinh}}(a\ T_{a}/c)\,}
Phase 4 : c / a
arsinh ( a T a / c ) {\displaystyle...
- /2<x<\pi /2} as
arsinh ( tan x ) , {\displaystyle \operatorname {
arsinh} (\tan x),}
where arsinh {\displaystyle \operatorname {
arsinh} } is the inverse...
-
equations x = a
arsinh ( p a ) + T 0 E p + α , y = a 2 + p 2 + T 0 2 E a p 2 + β . {\displaystyle {\begin{aligned}x&=a\operatorname {
arsinh} \left({\frac...
- + r x | = r − a
arsinh a x {\displaystyle \int {\frac {r\,dx}{x}}=r-a\ln \left|{\frac {a+r}{x}}\right|=r-a\,\operatorname {
arsinh} {\frac {a}{x}}}...
- b 2 [ θ 1 + θ 2 +
arsinh θ ] θ 1 θ 2 . {\displaystyle {\frac {b}{2}}\left[\theta \,{\sqrt {1+\theta ^{2}}}+\operatorname {
arsinh} \theta \right]_{\theta...
