Returns the hyperbolic sine of a Complex.

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

Syntax

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

Parameters

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

Return Value

A newly constructed Complex initialized to the hyperbolic sine of the argument.

Remarks

If z = x+iy,

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

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

\sinh(+0 + i\infty ) returns \pm 0 + i\NaN (where the sign of the real part of the result is unspecified).

\sinh(+\infty + i0) returns +\infty + i0.

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

\sinh(+\infty + iy) returns +\infty [\cos(y)+i\sin(y)], for positive finite y.

\sinh(x + i\infty ) returns \NaN + i\NaN, for positive finite x.

\sinh(+0 + i\NaN) returns \pm 0 + i\NaN (where the sign of the real part of the result is unspecified).

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

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

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

\sinh(\NaN + iy) returns \NaN + i\NaN, for all nonzero numbers y.

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

See Also