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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.16.16.0001.01









  


  










Input Form





WeierstrassSigma[i, z \[PlusMinus] Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}] == (\[MinusPlus]Exp[(\[PlusMinus]Subscript[\[Eta], i]) z]) WeierstrassSigma[j, Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[k, Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}] (WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}]/ WeierstrassSigma[Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}]) /; Element[{i, j, k}, {1, 2, 3}] && i != j != k










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", RowBox[List["z_", "\[PlusMinus]", SubscriptBox["\[Omega]_", "i_"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["\[MinusPlus]", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[PlusMinus]", SubscriptBox["\[Eta]", "i"]]], " ", "z"]]]]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["j", ",", SubscriptBox["\[Omega]\[Omega]", "i"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", SubscriptBox["\[Omega]\[Omega]", "i"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["\[Omega]\[Omega]", "i"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j", ",", "k"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j", "\[NotEqual]", "k"]]]]]]]]]]










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





2001-10-29





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