ASECH

Purpose:

Calculates the inverse hyperbolic secant of any expression.

Syntax:

ASECH(val)

val

-

A scalar, series or table.

Returns:

A scalar, series, or table.

Example:

asech(0.01..0.01..1);gridhv;griddot

 

 

image\asechpic01.gif

 

displays the inverse hyperbolic secant from 0.01 to 1.

Example:

asech(0.5)

 

returns 1.3169579.

Example:

asech(-2..0.1..2)

 

returns a 41 point complex series.

Remarks:

The inverse hyperbolic secant is defined as:

 

image\asech01.gif

 

for all complex z. The function is multi-valued and this definition places the branch cut in the complex plane at [-∞, 0] and [1, ∞].

 

image\asech02.gif

 

For x < 0 or x > 1, asech(x) returns a complex result.

 

SETDEGREE and SETRADIAN have no effect on this function because it always operates in radians.

See Also:

ACOSH

ASEC

GASECH

SEC

SECH

TRIGONOMETRIC FUNCTIONS