-
angle measure, for
example arsinh ( sinh a ) = a {\displaystyle \operatorname {
arsinh} (\sinh a)=a} and sinh (
arsinh x ) = x . {\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...
- functions. The
inverse hyperbolic functions are: area
hyperbolic sine "
arsinh" (also
denoted "sinh−1", "asinh" or
sometimes "arcsinh") area hyperbolic...
- α e − δ x − θ
arsinh ( x ) , {\displaystyle P(x)={\frac {M}{1+\alpha e^{-\delta x-\theta \operatorname {
arsinh} (x)}}},}
where arsinh {\displaystyle...
- gd − 1 φ =
arsinh ( tan φ ) , {\displaystyle \operatorname {gd} ^{-1}\varphi =\operatorname {
arsinh} (\tan \varphi ),} and
arsinh {\displaystyle...
- + 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}}}...
- {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...
- arguments. An
alternative expression in
terms of the
inverse hyperbolic sine
arsinh is
numerically well
behaved for real
arguments | ϕ | < 1 2 π {\textstyle...
- 2 = c tanh {
arsinh ( u 0 γ 0 + α T c ) } X ( T ) = X 0 + c 2 α ( 1 + ( u 0 γ 0 + α T c ) 2 − γ 0 ) = X 0 + c 2 α { cosh [
arsinh ( u 0 γ 0 + α...
- {\textstyle p_{1}} and p 2 , {\textstyle p_{2},}
arsinh x = ln ( x + x 2 + 1 ) {\textstyle \operatorname {
arsinh} x=\ln {\bigl (}x+{\sqrt {x^{2}+1}}{\bigr...
