<?xml version="1.0" encoding="UTF-8"?>
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 * Copyright (C) 2019 - Samuel GOUGEON
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
          xmlns:scilab="http://www.scilab.org" xml:id="atanh" xml:lang="ja">
    <refnamediv>
        <refname>atanh</refname>
        <refpurpose>双曲線逆正接</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>t = atanh(x)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>引数</title>
        <variablelist>
            <varlistentry>
                <term>x, t</term>
                <listitem>
                    <para>実数または複素数のベクトル/行列</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            ベクトル<varname>t</varname>の要素は,ベクトル<varname>x</varname>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,<literal>[-1,1]</literal>です.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <para>
            With input real numbers:
        </para>
        <programlisting role="example"><![CDATA[
x = [-%inf -2 -1 -0.5 0 0.5 1 2 3 %inf];
[x ; atanh(tanh(x))]
atanh(x')
 ]]></programlisting>
    <screen><![CDATA[
--> [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
]]></screen>
        <para>
            With input complex numbers:
        </para>
        <programlisting role="example"><![CDATA[
x = [-1-%i, -%i, 0, %i, %i+1];
[x; tanh(atanh(x)) ; atanh(tanh(x))]
atanh(x.')
 ]]></programlisting>
    <screen><![CDATA[
--> [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
]]></screen>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="tanh">tanh</link>
            </member>
        </simplelist>
    </refsection>
    <refsection role="history">
        <title>履歴</title>
        <revhistory>
            <revision>
                <revnumber>6.0</revnumber>
                <revdescription>
                    <itemizedlist>
                        <listitem>
                            <literal>atanh(-1)</literal> is now always <literal>-Inf</literal>, and
                            <literal>atanh(1)</literal> always <literal>Inf</literal>.
                        </listitem>
                        <listitem>
                            For any real x>1, imag(atanh(x)) is now > 0.
                        </listitem>
                    </itemizedlist>
                </revdescription>
            </revision>
        </revhistory>
    </refsection>
</refentry>