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Scilabヘルプ >> Elementary Functions > Trigonometry > atanh

atanh

双曲線逆正接

呼び出し手順

t = atanh(x)

引数

x, t

実数または複素数のベクトル/行列

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.

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

参照

  • 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.
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Last updated:
Tue Jul 20 11:20:43 CEST 2021