asech — computes the element-wise inverse hyperbolic secant of the argument.
y = asech(x)
Computes the element-wise inverse hyperbolic secant of the argument. If the argument is real and have absolute value less than one the result is real.
The following equalities hold: asech(x) = acosh(1 ./ x)=
%i*csgn(%i*(1−1 ./ x))*asec(x)=csgn(%i*(1 − 1 ./
x))*(%pi/2*(%i+acsch(%i*x)))
| Kahan, W., "Branch cuts for complex elementary functions, or, Much ado about nothing's sign bit", Proceedings of the joing IMA/SIAM conference on The State of the Art in Numerical Analysis, University of Birmingham, A. Iserles and M.J.D. Powell, eds, Clarendon Press, Oxford, 1987, 165-210. |