ATANH

Type:

Analytic Function

 

 

Description:

Arc Hyperbolic Tangent Analytic Function: Returns the inverse hyperbolic tangent of the

 

argument.

 

 

 

For real arguments x > 1, ATANH returns the complex result obtained for the argument (x, 0).

 

For a real argument x=±1, an Infinite Result exception occurs. If flag –22 is set (no error), the

 

sign of the result (MAXR) matches that of the argument.

 

 

The inverse of TANH is a relation, not a function, since TANH sends more than one argument to

 

the same result. The inverse relation for TANH is expressed by ISOL as the general solution;

 

 

 

ATANH(Z)+π*i*n1

 

 

The function ATANH is the inverse of a part of TANH, a part defined by restricting the domain

 

of TANH such that:

 

 

 

•

each argument is sent to a distinct result, and

 

 

•

each possible result is achieved.

 

 

 

The points in this restricted domain of TANH are called the principal values of the inverse relation.

 

ATANH in its entirety is called the principal branch of the inverse relation, and the points sent by

 

ATANH to the boundary of the restricted domain of TANH form the branch cuts of ATANH.

 

The principal branch used by the calculator for ATANH was chosen because it is analytic in the

 

regions where the arguments of the real-valuedfunction are defined. The branch cut for the

 

complex-valued ATANH function occurs where the corresponding real-valued function is

 

undefined. The principal branch also preserves most of the important symmetries.

 

The graph for ATANH can be found from the graph for ATAN (see ATAN) and the relationship

 

atanh z = –iatan iz.

 

 

Access:

…ÑHYPERBOLIC ATAN

(Ñis the right-shift of the 8key).

Flags:

Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

Level 1/Item 1

 

 

 

 

 

 

 

 

 

z

→

atanh z

 

 

 

'symb'

→

'ATANH(symb)'

 

 

 

 

 

See also:

ACOSH, ASINH, ISOL, TANH

 

 

 

 

 

 

 

 

ATICK

Command

 

 

Type:

 

 

Description: Axes Tick-Mark Command: Sets the axes tick-mark annotation in the reserved variable PPAR.

Given x, ATICK sets the tick-mark annotation to x units on both the x- and the y-axis. For example, 2 would place tick-marks every 2 units on both axes.

Given #n, ATICK sets the tick-mark annotation to #n pixels on both the x- and the y-axis. For example, #5 would place tick-marks every 5 pixels on both axes.

Given { x y }, ATICK sets the tick-mark unit annotation for each axis individually. For example,

{10 3 } would mark the x-axis at every multiple of 10 units, and the y-axis at every multiple of 3 units.

Given { #n #m } ATICK sets the tick-mark pixel annotation for each axis individually. For example, {#6 #2 } would mark the x-axis every 6 pixels, and the y-axis every 2 pixels.

Access: …µATICK

3-22 Full Command and Function Reference