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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.15.16.0002.01









  


  










Input Form





WeierstrassSigma[Subscript[z, 1] + Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] == Exp[Subscript[z, 1] WeierstrassZeta[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] - (Subscript[z, 1]^2/2) WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]] WeierstrassSigma[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] Product[(1 - Subscript[z, 1]/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3] - Subscript[z, 2])) Exp[Subscript[z, 1]/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3] - Subscript[z, 2]) + (1/2) (Subscript[z, 1]^2/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3] - Subscript[z, 2])^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["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SubsuperscriptBox["zz", "1", "2"], " ", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox[SubscriptBox["zz", "1"], RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]], "-", SubscriptBox["zz", "2"]]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SubscriptBox["zz", "1"], RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]], "-", SubscriptBox["zz", "2"]]]], "+", FractionBox[SubsuperscriptBox["zz", "1", "2"], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]], "-", SubscriptBox["zz", "2"]]], ")"]], "2"]]]]]]]]]]]]]]]]]]]










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





2001-10-29





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