* Bug 16290: %sn() set obsolete
[scilab.git] / scilab / modules / special_functions / help / en_US / delip.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <!--
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13  * along with this program.
14  *
15  -->
16 <!--  module: signal_processing  -->
17 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="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="delip" xml:lang="en">
18     <refnamediv>
19         <refname>delip</refname>
20         <refpurpose>complete and incomplete elliptic integral of first
21             kind
22         </refpurpose>
23     </refnamediv>
24     <refsynopsisdiv>
25         <title>Syntax</title>
26         <synopsis>[r]=delip(x,ck)</synopsis>
27     </refsynopsisdiv>
28     <refsection>
29         <title>Arguments</title>
30         <variablelist>
31             <varlistentry>
32                 <term>x</term>
33                 <listitem>
34                     <para>real vector/matrix with nonnegative elements</para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>ck</term>
39                 <listitem>
40                     <para>real number between -1 and 1</para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>r</term>
45                 <listitem>
46                     <para>real or complex number (or vector/matrix) with the same size as
47                         <literal>x</literal>
48                     </para>
49                 </listitem>
50             </varlistentry>
51         </variablelist>
52     </refsection>
53     <refsection>
54         <title>Description</title>
55         <para>The elliptic integral of the first kind with parameter
56             <literal>ck</literal> is defined as follow:
57         </para>
58         <para>
59             <inlinemediaobject>
60                 <imageobject>
61                     <imagedata align="center">
62                         <mml:math>
63                             <mml:semantics>
64                                 <mml:mrow>
65                                     <mml:munderover>
66                                         <mml:mo mml:stretchy="false">∫</mml:mo>
67                                         <mml:mn>0</mml:mn>
68                                         <mml:mi>x</mml:mi>
69                                     </mml:munderover>
70                                     <mml:mfrac>
71                                         <mml:mi mml:fontstyle="italic">dt</mml:mi>
72                                         <mml:msqrt>
73                                             <mml:mrow>
74                                                 <mml:mrow>
75                                                     <mml:mo mml:stretchy="false">(</mml:mo>
76                                                     <mml:mrow>
77                                                         <mml:mn>1</mml:mn>
78                                                         <mml:mo mml:stretchy="false">−</mml:mo>
79                                                         <mml:msup>
80                                                             <mml:mi>t</mml:mi>
81                                                             <mml:mn>2</mml:mn>
82                                                         </mml:msup>
83                                                     </mml:mrow>
84                                                     <mml:mo mml:stretchy="false">)</mml:mo>
85                                                 </mml:mrow>
86                                                 <mml:mrow>
87                                                     <mml:mo mml:stretchy="false">(</mml:mo>
88                                                     <mml:mrow>
89                                                         <mml:mrow>
90                                                             <mml:mn>1</mml:mn>
91                                                             <mml:mo mml:stretchy="false">−</mml:mo>
92                                                             <mml:msubsup>
93                                                                 <mml:mi>c</mml:mi>
94                                                                 <mml:mi>k</mml:mi>
95                                                                 <mml:mn>2</mml:mn>
96                                                             </mml:msubsup>
97                                                         </mml:mrow>
98                                                         <mml:msup>
99                                                             <mml:mi>t</mml:mi>
100                                                             <mml:mn>2</mml:mn>
101                                                         </mml:msup>
102                                                     </mml:mrow>
103                                                     <mml:mo mml:stretchy="false">)</mml:mo>
104                                                 </mml:mrow>
105                                             </mml:mrow>
106                                         </mml:msqrt>
107                                     </mml:mfrac>
108                                 </mml:mrow>
109                                 <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{
110                                     (1-t^2)(1-c_k^2 t^2)}}
111                                 </mml:annotation>
112                             </mml:semantics>
113                         </mml:math>
114                     </imagedata>
115                 </imageobject>
116             </inlinemediaobject>
117         </para>
118         <para>
119             Where <literal>x</literal> is real and positive,
120             <literal>ck</literal> is in <literal>[-1 1]</literal>.
121         </para>
122         <para>
123             If <literal>x</literal>  is less than 1 the result is real.
124         </para>
125         <para>
126             When called with <literal>x</literal> a vector/matrix <literal>r</literal>
127             is evaluated for each entry of <literal>x</literal>.
128         </para>
129     </refsection>
130     <refsection>
131         <title>Examples</title>
132         <programlisting role="example"><![CDATA[
133 ck=0.5;
134 delip([1,2],ck)
135 deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))')
136 intg(0,1,f)    //OK since real solution!
137  ]]></programlisting>
138     </refsection>
139     <refsection role="see also">
140         <title>See also</title>
141         <simplelist type="inline">
142             <member>
143                 <link linkend="amell">amell</link>
144             </member>
145             <member>
146                 <link linkend="ellipj">ellipj</link>
147             </member>
148             <member>
149                 <link linkend="percentk">%k</link>
150             </member>
151         </simplelist>
152     </refsection>
153 </refentry>