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WeierstrassZeta




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Primary definition





http://functions.wolfram.com/09.17.02.0001.01









  


  








Input Form





WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] == 1/z + Sum[If[{m, n} == {0, 0}, 0, 1/(z - 2 m Subscript[\[Omega], 1] - 2 n Subscript[\[Omega], 3]) + 1/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3]) + z/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3])^2], {m, -Infinity, Infinity}, {n, -Infinity, Infinity}] /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}]








Standard Form





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MathML Form







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</ms> <ms> 3 </ms> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> 2 </ms> </apply> </apply> </list> </apply> <ms> + </ms> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> m </ms> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> n </ms> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 3 </ms> </apply> </list> </apply> </list> </apply> </apply> <ms> + </ms> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> m </ms> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> n </ms> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 3 </ms> </apply> </list> </apply> </list> </apply> </apply> </list> </apply> </list> </apply> <ms> /; 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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["1", "z"], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["m", ",", "n"]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]]]], ",", "0", ",", RowBox[List[FractionBox["1", RowBox[List["z", "-", RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "-", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]]], "+", FractionBox["1", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]]], "+", FractionBox["z", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], "2"]]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]]]]]]]]


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





2001-10-29