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# atanh

### 呼び出し手順

`t = atanh(x)`

x, t

### 説明

ベクトル`t`の要素は,ベクトル`x`の対応する要素の双曲線逆正接となります. 実数関数の場合,定義域は,`[-1,1]`です.

### 例

With input real numbers:

```x = [-%inf -2 -1 -0.5 0 0.5 1 2 3 %inf];
[x ; atanh(tanh(x))]
atanh(x')```
```--> [x ; atanh(tanh(x))]
ans  =
-Inf  -2.  -1.  -0.5   0.   0.5   1.   2.   3.   Inf
-Inf  -2.  -1.  -0.5   0.   0.5   1.   2.   3.   Inf

--> atanh(x')
ans  =
0.        + 1.5707963i
-0.5493061 + 1.5707963i
-Inf       + 0.i
-0.5493061 + 0.i
0.        + 0.i
0.5493061 + 0.i
Inf       + 0.i
0.5493061 + 1.5707963i
0.3465736 + 1.5707963i
0.        + 1.5707963i
```

With input complex numbers:

```x = [-1-%i, -%i, 0, %i, %i+1];
[x; tanh(atanh(x)) ; atanh(tanh(x))]
atanh(x.')```
```--> [x; tanh(atanh(x)) ; atanh(tanh(x))]
ans  =

-1. - i     0. - i     0. + 0.i   0. + i     1. + i
-1. - i     0. - i     0. + 0.i   0. + i     1. + i
-1. - i     0. - i     0. + 0.i   0. + i     1. + i

--> atanh(x.')
ans  =

-0.4023595 - 1.017222i
0.        - 0.7853982i
0.        + 0.i
0.        + 0.7853982i
0.4023595 + 1.017222i
```

• tanh — 双曲線正接

### 履歴

 バージョン 記述 6.0 `atanh(-1)` is now always `-Inf`, and `atanh(1)` always `Inf`. For any real x>1, imag(atanh(x)) is now > 0.