- {1+u^{2}}}\right)}
arcosh u ±
arcosh v =
arcosh ( u v ± ( u 2 − 1 ) ( v 2 − 1 ) ) {\displaystyle \operatorname {
arcosh} u\pm \operatorname {
arcosh} v=\operatorname...
-
denoted "sinh−1", "asinh" or
sometimes "arcsinh") area
hyperbolic cosine "
arcosh" (also
denoted "cosh−1", "acosh" or
sometimes "arccosh") area hyperbolic...
- -2)} ∫
arcosh ( a x ) d x = x
arcosh ( a x ) − a x + 1 a x − 1 a + C {\displaystyle \int \operatorname {
arcosh} (ax)\,dx=x\operatorname {
arcosh} (ax)-{\frac...
- ) ↦ ( v (
arcosh y ) cos x , v (
arcosh y ) sin x , u (
arcosh y ) ) {\displaystyle (x,y)\mapsto {\big (}v(\operatorname {
arcosh} y)\cos x,v(\operatorname...
- C=x\operatorname {arcsec}(x)-\operatorname {
arcosh} |x|+C} ∫
arcsec ( a x ) d x = x
arcsec ( a x ) − 1 a
arcosh | a x | + C {\displaystyle \int \operatorname...
-
hyperbolic functions:
arsinh x ,
arcosh x , {\displaystyle \operatorname {arsinh} x,\ \operatorname {
arcosh} x,} etc. All
functions obtained by adding...
- of this
integral yields z = f ( ζ ) = C + K
arcosh ζ , {\displaystyle z=f(\zeta )=C+K\operatorname {
arcosh} \zeta ,}
where C is a (complex)
constant of...
- π
arcosh ( D d ) {\displaystyle L={\frac {\mu }{\ \pi \ }}\ \operatorname {
arcosh} \left({\frac {\ D\ }{d}}\right)} G = π σ
arcosh ( ...
-
computed as: s = b ∫
arcosh x 1 a
arcosh x 2 a 1 + ( 1 + a 2 b 2 ) sinh 2 v d v . {\displaystyle s=b\int _{\operatorname {
arcosh} {\frac {x_{1}}{a}}}^{\operatorname...
- π ε ℓ
arcosh ( R 1 2 + R 2 2 − d 2 2 R 1 R 2 ) {\displaystyle \ {\mathcal {C}}={\frac {2\pi \varepsilon \ell }{\ \operatorname {
arcosh} \left({\frac...
