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JacobiAmplitude




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > General characteristics > Symmetries and periodicities > Periodicity





http://functions.wolfram.com/09.24.04.0011.01









  


  








Input Form





JacobiAmplitude[z + 2 I EllipticK[1 - m], m] == JacobiAmplitude[z, m] /; m > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["z", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]]]], ",", "m"]], "]"]], "\[Equal]", " ", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]]]], "/;", RowBox[List["m", ">", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["z_", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m_"]], "]"]]]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "/;", RowBox[List["m", ">", "0"]]]]]]]]


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





2007-05-02