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EllipticK




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/08.02.06.0026.01









  


  








Input Form





EllipticK[z] \[Proportional] (Pi/2) (1 + z/4 + (9 z^2)/64 + O[z^3])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EllipticK", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["\[Pi]", "2"], RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "4"], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox["z", "2"]]], "64"], "+", RowBox[List["O", "[", SuperscriptBox["z", "3"], "]"]]]], ")"]]]]]]]]








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> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 64 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> EllipticK </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 64 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "4"], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox["z", "2"]]], "64"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "3"]]], ")"]]]]]]]]


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





2007-05-02