asech
computes the element-wise inverse hyperbolic secant of the argument.
Syntax
y = asech(x)
Arguments
- x
a real or complex array.
- y
a real or complex array.
Description
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)))
.
See also
- sech — computes the element-wise hyperbolic secant of the argument
References
- 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.
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