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WeierstrassZeta






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Transformations > Multiple arguments > Argument involving numeric multiples of variable > Double angle formulas





http://functions.wolfram.com/09.17.16.0007.01









  


  










Input Form





WeierstrassZeta[2 z, {Subscript[g, 2], Subscript[g, 3]}] == (1/2) (WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassZeta[z - Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassZeta[z - Subscript[\[Omega], 2], {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassZeta[ z - Subscript[\[Omega], 3], {Subscript[g, 2], Subscript[g, 3]}])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["2", " ", "z"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "1"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "3"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["2", " ", "z_"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "1"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "-", SubscriptBox["\[Omega]", "3"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], ")"]]]]]]]]










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





2001-10-29