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# acsch

computes the element-wise inverse hyperbolic cosecant of the argument.

### Calling Sequence

`y = acsch(x)`

### Arguments

x

Real or complex array.

y

Real or complex array.

### Description

Computes the element-wise inverse hyperbolic cotsecant of the argument. For real argument with absolute value greater than 1 the result is real.

The following equalities hold: ```acsch(z) = -acsch(-z) = asinh(1/z) = csgn(%i+1/z)*asech(-i*z)-%i*%pi/2 = %i*acsc(%i*z)```

### Examples

```x=linspace(1,20,200);
x=[-x(\$:-1:1) %nan x];
plot(x,acsch(x))```

### See Also

• csch — Computes the element-wise hyperbolic cosecant 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.

### Authors

• Serge Steer, INRIA
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