Complex.Cosh Method

IMSL .NET Numerical Libraries

ComplexCosh Method

Returns the hyperbolic cosh of a Complex.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static Complex Cosh(
	Complex z
)

Public Shared Function Cosh ( 
	z As Complex
) As Complex

public:
static Complex Cosh(
	Complex z
)

static member Cosh : 
        z : Complex -> Complex

Parameters

z: Type: Imsl.MathComplex
A Complex object.

Return Value

Type: Complex
A newly constructed Complex initialized to the hyperbolic cosine of the argument.

Remarks

If z = x+iy,

$\cosh(\bar{z}) = \overline{\cosh(z)}$ and cosh is even.

$\cosh(+0 + i0)$ returns .

$\cosh(+0 + i\infty )$ returns $\NaN \pm i0$ (where the sign of the imaginary part of the result is unspecified).

$\cosh(+\infty + i0)$ returns $+\infty + i0$ .

$\cosh(+\infty + i\infty )$ returns $+\infty + i\NaN$ .

$\cosh(x + i\infty )$ returns $\NaN + i\NaN$ , for finite nonzero x.

$\cosh(+\infty + iy)$ returns $+\infty [\cos(y)+i\sin(y)]$ , for finite nonzero y.

$\cosh(+0 + i\NaN)$ returns $\NaN \pm i0$ (where the sign of the imaginary part of the result is unspecified).

$\cosh(+\infty + i\NaN)$ returns $+\infty + i\NaN$ .

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

$\cosh(\NaN + i0)$ returns $\NaN \pm i0$ (where the sign of the imaginary part of the result is unspecified).

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

$\cosh(\NaN + i\NaN)$ returns $\NaN + i\NaN$ .

See Also

Reference

Complex Structure

Imsl.Math Namespace

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