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WeierstrassZeta




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Series representations > Other series representations





http://functions.wolfram.com/09.17.06.0012.01









  


  








Input Form





WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] == (Subscript[\[Eta], i] z)/Subscript[\[Omega], i] + (Pi/(2 Subscript[\[Omega], i])) Cot[(Pi z)/(2 Subscript[\[Omega], i])] + (Pi/(2 Subscript[\[Omega], i])) Sum[If[k == 0, 0, Cot[Pi ((z - 2 k Subscript[\[Omega], j])/ (2 Subscript[\[Omega], i]))] + Cot[Pi ((k Subscript[\[Omega], j])/Subscript[\[Omega], i])]], {k, -Infinity, Infinity}] /; Element[{i, j}, {1, 2, 3}] && i != j








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SubscriptBox["\[Eta]", "i"], " ", "z"]], SubscriptBox["\[Omega]", "i"]], "+", RowBox[List[FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "i"]]]], " ", RowBox[List["Cot", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "i"]]]], "]"]]]], "+", RowBox[List[FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "i"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List["k", "\[Equal]", "0"]], ",", "0", ",", RowBox[List[RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", FractionBox[RowBox[List["z", "-", RowBox[List["2", "k", " ", SubscriptBox["\[Omega]", "j"]]]]], RowBox[List["2", SubscriptBox["\[Omega]", "i"]]]]]], "]"]], "+", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", FractionBox[RowBox[List["k", " ", SubscriptBox["\[Omega]", "j"]]], SubscriptBox["\[Omega]", "i"]]]], "]"]]]]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "\[And]", RowBox[List["i", "\[NotEqual]", "j"]]]]]]]]








MathML Form







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</ci> <ci> j </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> i </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <cot /> <apply> <times /> <pi /> <apply> <times /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> j </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </ci> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SubscriptBox["\[Eta]", "i"], " ", "z"]], SubscriptBox["\[Omega]", "i"]], "+", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["Cot", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "i"]]]], "]"]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "i"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List["k", "\[Equal]", "0"]], ",", "0", ",", RowBox[List[RowBox[List["Cot", "[", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["2", " ", "k", " ", SubscriptBox["\[Omega]", "j"]]]]], ")"]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "i"]]]], "]"]], "+", RowBox[List["Cot", "[", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["k", " ", SubscriptBox["\[Omega]", "j"]]], ")"]]]], SubscriptBox["\[Omega]", "i"]], "]"]]]]]], "]"]]]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "i"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j"]]]]]]]]]]


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





2001-10-29