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WeierstrassZeta




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Representations through equivalent functions > With related functions > Involving theta functions





http://functions.wolfram.com/09.17.27.0005.01









  


  








Input Form





WeierstrassZeta[z + Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}] == Subscript[\[Eta], i] + (Subscript[\[Eta], 1] z)/ Subscript[\[Omega], 1] + (Pi/(2 Subscript[\[Omega], 1])) (EllipticThetaPrime[i + 1, (Pi z)/(2 Subscript[\[Omega], 1]), q]/ EllipticTheta[i + 1, (Pi z)/(2 Subscript[\[Omega], 1]), q]) /; Element[i, {1, 2, 3}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "+", SubscriptBox["\[Omega]", "i"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[SubscriptBox["\[Eta]", "i"], "+", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], " ", "z"]], SubscriptBox["\[Omega]", "1"]], "+", RowBox[List[FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], " ", FractionBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]]]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "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> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <msub> <mi> &#969; </mi> <mi> i </mi> </msub> </mrow> <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> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[&quot;z&quot;, &quot;+&quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;i&quot;]]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <msub> <mi> &#951; </mi> <mi> i </mi> </msub> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> </mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <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> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <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> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> i </mi> <mo> &#8712; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassZeta </ci> <apply> <plus /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> i </ci> </apply> </apply> <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> <ci> Subscript </ci> <ci> &#951; </ci> <ci> i </ci> </apply> <apply> <times /> <ci> z </ci> <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> <times /> <pi /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <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> <ci> q </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <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> <ci> q </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <ci> i </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z_", "+", SubscriptBox["\[Omega]_", "i_"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["\[Eta]", "i"], "+", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], " ", "z"]], SubscriptBox["\[Omega]\[Omega]", "1"]], "+", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]], ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]], ",", "q"]], "]"]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]


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





2001-10-29