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JacobiAmplitude




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Series representations > Generalized power series > Expansions at m==1





http://functions.wolfram.com/09.24.06.0017.01









  


  








Input Form





JacobiAmplitude[z, m] \[Proportional] 2 ArcTan[E^z] - Pi/2 + O[m - 1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTan", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]]]], "-", FractionBox["\[Pi]", "2"], "+", RowBox[List["O", "[", RowBox[List["m", "-", "1"]], "]"]]]]]]]]








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> &#8733; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctan /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </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[RowBox[List["2", " ", RowBox[List["ArcTan", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]]]], "-", FractionBox["\[Pi]", "2"], "+", RowBox[List["O", "[", RowBox[List["m", "-", "1"]], "]"]]]]]]]]


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





2007-05-02