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)

Sample

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.