[doc] Misc. small improvements
[scilab.git] / scilab / modules / special_functions / help / en_US / delip.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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16 <!--  module: signal_processing  -->
17 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
18           xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
19           xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
20           xmlns:scilab="http://www.scilab.org" xml:id="delip" xml:lang="en">
21     <refnamediv>
22         <refname>delip</refname>
23         <refpurpose>complete and incomplete elliptic integral of first
24             kind
25         </refpurpose>
26     </refnamediv>
27     <refsynopsisdiv>
28         <title>Syntax</title>
29         <synopsis>r = delip(x, ck)</synopsis>
30     </refsynopsisdiv>
31     <refsection>
32         <title>Arguments</title>
33         <variablelist>
34             <varlistentry>
35                 <term>x</term>
36                 <listitem>
37                     <para>real vector/matrix with nonnegative elements</para>
38                 </listitem>
39             </varlistentry>
40             <varlistentry>
41                 <term>ck</term>
42                 <listitem>
43                     <para>real number between -1 and 1</para>
44                 </listitem>
45             </varlistentry>
46             <varlistentry>
47                 <term>r</term>
48                 <listitem>
49                     <para>real or complex number (or vector/matrix) with the same size as
50                         <literal>x</literal>
51                     </para>
52                 </listitem>
53             </varlistentry>
54         </variablelist>
55     </refsection>
56     <refsection>
57         <title>Description</title>
58         <para>
59             The elliptic integral of the first kind with parameter
60             <literal>ck</literal> is defined as follow:
61             <latex style="display" alt="integral_0^x dt / sqrt((1 - t^2)(1 - c_k^2 t^2))">
62                 \int_0^x {dt \over {\sqrt{(1-t^2)(1-c_k^2\;t^2)}}
63             </latex>
64         </para>
65         <para>
66             Where <literal>x</literal> is real and positive,
67             <literal>ck</literal> is in <literal>[-1 1]</literal>.
68         </para>
69         <para>
70             If <literal>x</literal>  is less than 1 the result is real.
71         </para>
72         <para>
73             When called with <literal>x</literal> a vector/matrix <literal>r</literal>
74             is evaluated for each entry of <literal>x</literal>.
75         </para>
76     </refsection>
77     <refsection>
78         <title>Examples</title>
79         <programlisting role="example"><![CDATA[
80 delip([1,2], 0.5)
81 deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))')
82 intg(0, 1, f)    // OK since real solution!
83  ]]></programlisting>
84     </refsection>
85     <refsection role="see also">
86         <title>See also</title>
87         <simplelist type="inline">
88             <member>
89                 <link linkend="amell">amell</link>
90             </member>
91             <member>
92                 <link linkend="ellipj">ellipj</link>
93             </member>
94             <member>
95                 <link linkend="percentk">%k</link>
96             </member>
97         </simplelist>
98     </refsection>
99 </refentry>