    # atanh

This function computes the inverse hyperbolic tan of a number.

# ATANH

## NAME

atanh - This function computes the inverse hyperbolic tan of a number.

atanh(number)

## DESCRIPTION

This mathematical function allows the user to compute the inverse hyperbolic tan of an argument defined between -1 to 1. This is not a periodic function. It gives the hyperbolic angle to the value of the hyperbolic function which is written as argument of the atanh. In other words, the answer is the value whose hyperbolic tan is the argument. It returns a value only in the 1st or 3rd quadrant of the xy plane, meaning that if x<0, y<0 and if x>0, y>0.

## PARAMETERS

number
Specify the number (float) used as argument for the atanh function.

## RETURN

The atanh value of the argument.

## EXAMPLES

Note: In the followings examples, the _ between the { should be removed to make it work.

```One can use this function with positive integers:

test(q(res={_{atanh(0.99);}}.),q(res=2.64665.));

With negative integers:

test(q(res={_{atanh(-0.99);}}.),q(res=-2.64665.));

Note that atanh(x)=atanh(-x).

With big integers:

test(q(res={_{atanh(45);}}.),q(res=NAN.));

Since the only possible answers of the tanh are defined between -1 and 1, an
argument greater than these numbers returns not a number. However, it has an
answer, a complex one: 0,02+1,57i, where i is the imaginary number.

test(q(res={_{atanh(1);}}.),q(res=INF.));

Here is another limit. Since it is defined between -1 and 1, 1 gives the
greatest value possible. Here this value is infinite.

With other variables:

test(q(res={_{
%include "/includes/extenso.sn";
a=0.99627;
atanh(a);
}}.),
q(res=PI.));

With another trigonometric function:

test(q(res={_{
%include "/includes/extenso.sn";
a=sin(0);
atanh(a);
}}.),
q(res=0.));

With an array:

test(q(res={_{atanh(.99,0,1);}}.),q(res=\[2.64665,0,INF\].));
```