[doc] misc. fix & improvements
[scilab.git] / scilab / modules / elementary_functions / help / en_US / trigonometry / atanh.xml
index b5f40b4..60dce6f 100644 (file)
  * along with this program.
  *
  -->
-<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="en">
+<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="en">
     <refnamediv>
         <refname>atanh</refname>
         <refpurpose>hyperbolic tangent inverse</refpurpose>
             evaluate an elementary mathematical function outside its definition domain
             in the real case, then the complex extension is used (with a complex
             result). The most famous example being the <function>sqrt</function> function (try
-            <code>sqrt(-1)</code>!). This approach have some drawbacks when you
-            evaluate the function at a singular point which may led to different
-            results when the point is considered as real or complex. For the
-            <function>atanh</function> this occurs for <literal>-1</literal> and
-            <literal>1</literal> because the at these points the imaginary part do not
+            <code>sqrt(-1)</code>!).
+        </para>
+        <para>
+            This approach has some drawbacks when you
+            evaluate the function at a singular point which may lead to different
+            results when the point is considered as real or complex.
+        </para>
+        <para>
+            For <literal>atanh()</literal>, this occurs for <literal>-1</literal> and
+            <literal>1</literal>, because at these points the imaginary part does not
             converge and so <literal>atanh(1) = +Inf + i NaN</literal> while
-            <literal>atanh(1) = +Inf</literal> for the real case (as lim <literal>x-&gt;1</literal>  of
-            <code>atanh(x)</code>). So when you evaluate this function on the vector <literal>[1 2]</literal>
+            <literal>atanh(1) = +Inf</literal> for the real case (as lim <literal>x-&gt;1</literal>
+            of <code>atanh(x)</code>).
+        </para>
+        <para>
+            So when you evaluate this function on the vector <literal>[1 2]</literal>
             then like <literal>2</literal> is outside the definition
             domain, the complex extension is used for all the vector and you get
-            <literal>atanh(1) = +Inf + i NaN</literal> while you get <literal>atanh(1)
-                = +Inf
-            </literal>
-            with <literal>[1 0.5]</literal> for instance.
+            <literal>atanh(1) = +Inf + i NaN</literal> while you get
+            <literal>atanh(1) = +Inf</literal> with <literal>[1, 0.5]</literal> for instance.
         </para>
     </refsection>
     <refsection>