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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[1,z,q] > Specific values > Specialized values > For fixed q





http://functions.wolfram.com/09.05.03.0005.01









  


  








Input Form





EllipticThetaPrime[1, 0, q]^8 == ((2 Subscript[\[Omega], 1])/Pi)^12 (Subscript[e, 2] - Subscript[e, 3])^2 (Subscript[e, 1] - Subscript[e, 2])^ 2 (Subscript[e, 1] - Subscript[e, 3])^2 /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 3] && \[Tau] == Subscript[\[Omega], 3]/ Subscript[\[Omega], 1] && q == E^(\[Tau] Pi I) && Subscript[e, \[Alpha]] == WeierstrassP[Subscript[\[Omega], \[Alpha]], {Subscript[g, 2], Subscript[g, 3]}]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "0", ",", "q_"]], "]"]], "8"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]], "\[Pi]"], ")"]], "12"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["e", "2"], "-", SubscriptBox["e", "3"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "2"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]], ")"]], "2"]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "3"]]]]], "&&", RowBox[List["\[Tau]", "\[Equal]", FractionBox[SubscriptBox["\[Omega]", "3"], SubscriptBox["\[Omega]", "1"]]]], "&&", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Tau]", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], "&&", RowBox[List[SubscriptBox["e", "\[Alpha]"], "\[Equal]", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "\[Alpha]"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]]]]]


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





2001-10-29