Returns the inverse hyperbolic cosine (arc cosh) of a Complex, with a branch cut at values less than one along the real axis.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static Complex Acosh(
	Complex z
)
Visual Basic (Declaration)
Public Shared Function Acosh ( _
	z As Complex _
) As Complex
Visual C++
public:
static Complex Acosh(
	Complex z
)

Parameters

z
Type: Imsl.Math..::.Complex
A Complex object.

Return Value

A newly constructed Complex initialized to the inverse (arc) hyperbolic cosine of the argument. The real part of the result is non-negative and its imaginary part is in the interval [-i\pi,i\pi].

Remarks

Specifically, if z = x+iy,

\acosh(\bar{z}) = \overline{\acosh(z)}.

\acosh(\pm 0 + i0) returns +0 + i\pi/2.

\acosh(-\infty + i\infty ) returns +\infty + i3 \pi/4.

\acosh(+\infty + i\infty ) returns +\infty + i \pi/4.

\acosh(x + i\infty ) returns +\infty + i \pi/2, for finite x.

\acosh(-\infty + iy) returns +\infty + i \pi, for positive-signed finite y.

\acosh(+\infty + iy) returns +\infty + i0, for positive-signed finite y.

\acosh(\NaN + i\infty ) returns +\infty + i\NaN.

\acosh(\pm \infty + i\NaN) returns +\infty + i\NaN.

\acosh(x + i\NaN) returns \NaN + i\NaN, for finite x.

\acosh(\NaN + iy) returns \NaN + i\NaN, for finite y.

\acosh(\NaN + i\NaN) returns \NaN + i\NaN.

See Also