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<A NAME=ASECH>

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



<B>ASECH</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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<P>
<em>asech</em>represents the hyperbolic arccosecant of its argument. It takes 
an arbitrary scalar expression as its argument. The derivative of 
<em>asech</em> is known to the system. Numerical values may also be found by 
turning on the switch 
<A HREF=r37_0330.html>rounded</A>. 
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 <P> <H3> 
syntax: </H3>
<em>asech</em>(&lt;expression&gt;) or <em>asech</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>
asech a; 

  ASECH(A) 


asech(1); 

  0 


df(acosh(a**2),a); 

            4
  2*SQRT(- A  + 1)
  ---------------- 
         4
     A*(A  - 1)


int(asech(x),x); 

  INT(ASECH(X),X)

</TT></PRE><P>You may attach functionality by defining <em>asech</em> to be the 
inverse of 
<em>sech</em>. This is done by the commands 
<P><PRE><TT>
        put('sech,'inverse,'asech);
        put('asech,'inverse,'sech);
</TT></PRE><P><P>
<P>
You can write a procedure to attach integrals or other 
functions to <em>asech</em>. You may wish to add a check to see that its 
argument is properly restricted. 
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