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WeierstrassZeta






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Transformations > Addition formulas > Translation by half-periods





http://functions.wolfram.com/09.17.16.0004.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "1"]]], ")"]], " ", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List[SubscriptBox["zz", "1"], "+", SubscriptBox["zz", "2"], "-", RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "-", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]]], "-", FractionBox["1", RowBox[List[SubscriptBox["zz", "2"], "-", RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "-", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]]], "+", FractionBox[SubscriptBox["zz", "1"], SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "-", RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "-", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], "2"]]]], ")"]]]]]]]]]]]]










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





2001-10-29





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