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JacobiAmplitude




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Integral representations > On the real axis





http://functions.wolfram.com/09.24.07.0001.01









  


  








Input Form





JacobiAmplitude[z, m] == Integrate[JacobiDN[t, m], {t, 0, z}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["t", ",", "m"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> z </mi> </msubsup> <mrow> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> t </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> z </ci> </uplimit> <apply> <ci> JacobiDN </ci> <ci> t </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["t", ",", "m"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02