Returns the inverse hyperbolic sine (arc sinh) of a Complex, with branch cuts outside the interval [-i,i].

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

Syntax

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

Parameters

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

Return Value

A newly constructed Complex initialized to the inverse (arc) hyperbolic sine of the argument. Its imaginary part is in the interval [-i\pi/2,i\pi/2].

Remarks

Specifically, if z = x+iy,

\asinh(\bar{z}) = \overline{\asinh(z)} and asinh is odd.

\asinh(+0 + i0) returns 0 + i0.

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

\asinh(x + i\infty ) returns +\infty + i \pi/2 for positive-signed finite x.

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

\asinh(\NaN + i\infty ) returns \pm \infty + i\NaN (where the sign of the real part of the result is unspecified).

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

\asinh(\NaN + i0) returns \NaN + i0.

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

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

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

See Also