f1fadc42ae2ef238329be8310398d77928b951f4
[scilab.git] / scilab / modules / special_functions / help / fr_FR / delip.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <!--  module: signal_processing  -->
3 <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="fr">
4     <refnamediv>
5         <refname>delip</refname>
6         <refpurpose>intégrale elliptique complete ou incomplete du premier
7             type
8         </refpurpose>
9     </refnamediv>
10     <refsynopsisdiv>
11         <title>Séquence d'appel</title>
12         <synopsis>[r]=delip(x,ck)</synopsis>
13     </refsynopsisdiv>
14     <refsection>
15         <title>Paramètres</title>
16         <variablelist>
17             <varlistentry>
18                 <term>x</term>
19                 <listitem>
20                     <para>vecteur réel à éléments non négatifs</para>
21                 </listitem>
22             </varlistentry>
23             <varlistentry>
24                 <term>ck</term>
25                 <listitem>
26                     <para>scalaire entre -1 et 1</para>
27                 </listitem>
28             </varlistentry>
29             <varlistentry>
30                 <term>r</term>
31                 <listitem>
32                     <para>réel ou complexe (ou vecteur)</para>
33                 </listitem>
34             </varlistentry>
35         </variablelist>
36     </refsection>
37     <refsection>
38         <title>Description</title>
39         <para>L'integrale élliptique du premier type pour le paramètre
40             <literal>ck</literal> est définie par:
41         </para>
42         <para>
43             <inlinemediaobject>
44                 <imageobject>
45                     <imagedata>
46                         <mml:math>
47                             <mml:semantics>
48                                 <mml:mrow>
49                                     <mml:munderover>
50                                         <mml:mo mml:stretchy="false">∫</mml:mo>
51                                         <mml:mn>0</mml:mn>
52                                         <mml:mi>x</mml:mi>
53                                     </mml:munderover>
54                                     <mml:mfrac>
55                                         <mml:mi mml:fontstyle="italic">dt</mml:mi>
56                                         <mml:msqrt>
57                                             <mml:mrow>
58                                                 <mml:mrow>
59                                                     <mml:mo mml:stretchy="false">(</mml:mo>
60                                                     <mml:mrow>
61                                                         <mml:mn>1</mml:mn>
62                                                         <mml:mo mml:stretchy="false">−</mml:mo>
63                                                         <mml:msup>
64                                                             <mml:mi>t</mml:mi>
65                                                             <mml:mn>2</mml:mn>
66                                                         </mml:msup>
67                                                     </mml:mrow>
68                                                     <mml:mo mml:stretchy="false">)</mml:mo>
69                                                 </mml:mrow>
70                                                 <mml:mrow>
71                                                     <mml:mo mml:stretchy="false">(</mml:mo>
72                                                     <mml:mrow>
73                                                         <mml:mrow>
74                                                             <mml:mn>1</mml:mn>
75                                                             <mml:mo mml:stretchy="false">−</mml:mo>
76                                                             <mml:msubsup>
77                                                                 <mml:mi>c</mml:mi>
78                                                                 <mml:mi>k</mml:mi>
79                                                                 <mml:mn>2</mml:mn>
80                                                             </mml:msubsup>
81                                                         </mml:mrow>
82                                                         <mml:msup>
83                                                             <mml:mi>t</mml:mi>
84                                                             <mml:mn>2</mml:mn>
85                                                         </mml:msup>
86                                                     </mml:mrow>
87                                                     <mml:mo mml:stretchy="false">)</mml:mo>
88                                                 </mml:mrow>
89                                             </mml:mrow>
90                                         </mml:msqrt>
91                                     </mml:mfrac>
92                                 </mml:mrow>
93                                 <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{
94                                     (1-t^2)(1-c_k^2 t^2)}}
95                                 </mml:annotation>
96                             </mml:semantics>
97                         </mml:math>
98                     </imagedata>
99                 </imageobject>
100             </inlinemediaobject>
101         </para>
102         <para>
103             Où <literal>x</literal> est réel et positif,<literal>ck</literal>
104             est dans l'intervalle <literal>[-1 1]</literal>.
105         </para>
106         <para>
107             Si <literal>x</literal> est plus petit ou égal a 1 le resultat est
108             réel
109         </para>
110         <para>
111             Quand <literal>x</literal> est un vecteur <literal>r</literal> est
112             évalué pour chaque composante de <literal>x</literal>.
113         </para>
114     </refsection>
115     <refsection>
116         <title>Exemples</title>
117         <programlisting role="example"><![CDATA[
118 ck=0.5;
119 delip([1,2],ck)
120 deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))')
121 intg(0,1,f)    // OK puisque la solution est réelle !
122  ]]></programlisting>
123     </refsection>
124     <refsection role="see also">
125         <title>Voir aussi</title>
126         <simplelist type="inline">
127             <member>
128                 <link linkend="amell">amell</link>
129             </member>
130             <member>
131                 <link linkend="ellipj">ellipj</link>
132             </member>
133             <member>
134                 <link linkend="percentsn">%sn</link>
135             </member>
136         </simplelist>
137     </refsection>
138 </refentry>