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<A NAME=ATANH>

<TITLE>ATANH</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>ATANH</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The <em>atanh</em> operator returns the hyperbolic arctangent of its argument. 
The derivative of <em>asinh</em> and some simple transformations are known 
to the system. 
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<P>
 <P> <H3> 
syntax: </H3>
<em>atanh</em>(&lt;expression&gt;) or <em>atanh</em> &lt;simple\_expression&gt; 

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&lt;expression&gt; may be any scalar REDUCE expression, not an array, matrix or 

vector expression. &lt;simple\_expression&gt; must be a single identifier or 
begin with a prefix operator name. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
atanh aa; 

  ATANH(AA) 


atanh(1); 

  ATANH(1) 


df(atanh(x*y),y); 

     - X
  ----------
   2  2
  X *Y  - 1

</TT></PRE><P>A numeric value is not returned by <em>asinh</em> unless the switc
h 
<em>rounded</em> is on and its argument evaluates to a number. 
You may attach additional functionality by defining <em>atanh</em> to be the 
inverse of <em>tanh</em>. This is done by the commands 
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<P><PRE><TT>
        put('tanh,'inverse,'atanh);
        put('atanh,'inverse,'tanh);
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