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WeierstrassInvariants




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassInvariants[{w1,w3}] > Representations through equivalent functions > With related functions > Involving theta functions





http://functions.wolfram.com/09.19.27.0010.01









  


  








Input Form





Last[WeierstrassInvariants[{Subscript[\[Omega], 1], Subscript[\[Omega], 3]}]] == (Pi/(2 Subscript[\[Omega], 1]))^6 ((8/27) (EllipticTheta[2, 0, q]^12 + EllipticTheta[3, 0, q]^12) - (4/9) (EllipticTheta[2, 0, q]^4 + EllipticTheta[3, 0, q]^4) EllipticTheta[2, 0, q]^4 EllipticTheta[3, 0, q]^4) /; \[Tau] == Subscript[\[Omega], 3]/Subscript[\[Omega], 1] && q == E^(\[Tau] Pi I)








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Last", "[", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", SubscriptBox["\[Omega]_", "3"]]], "}"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]], ")"]], "6"], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["8", "27"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], "12"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "12"]]], ")"]]]], "-", RowBox[List[FractionBox["4", "9"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], "4"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], "4"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["\[Tau]", "\[Equal]", FractionBox[SubscriptBox["\[Omega]", "3"], SubscriptBox["\[Omega]\[Omega]", "1"]]]], "&&", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Tau]", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]]]]]]]


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





2001-10-29