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WeierstrassP




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Series representations > q-series





http://functions.wolfram.com/09.13.06.0003.01









  


  








Input Form





WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] == -(Subscript[\[Eta], 1]/Subscript[\[Omega], 1]) + (Pi/(2 Subscript[\[Omega], 1]))^2 Csc[(Pi z)/(2 Subscript[\[Omega], 1])]^ 2 - ((2 Pi^2)/Subscript[\[Omega], 1]^2) Sum[((k q^(2 k))/(1 - q^(2 k))) Cos[(k Pi z)/Subscript[\[Omega], 1]], {k, 1, Infinity}]








Standard Form





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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> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <msubsup> <mi> &#969; </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mfrac> <mrow> <mi> k </mi> <mo> &#8290; </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassP </ci> <ci> z </ci> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <ci> k </ci> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> k </ci> <pi /> <ci> z </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[SubscriptBox["\[Eta]", "1"], SubscriptBox["\[Omega]", "1"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["Csc", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], "]"]], "2"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List["k", " ", SuperscriptBox["q", RowBox[List["2", " ", "k"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["k", " ", "\[Pi]", " ", "z"]], SubscriptBox["\[Omega]", "1"]], "]"]]]], RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", " ", "k"]]]]]]]]]], SubsuperscriptBox["\[Omega]", "1", "2"]]]]]]]]


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





2001-10-29