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# 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)))``` .

### Examples

```x=1 ./ [1 2 -2 sqrt(2) -sqrt(2) 2/sqrt(3) -2/sqrt(3) -1];
asech(x)/%pi```

### 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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