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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[2,z,q] > Representations through equivalent functions > With related functions > Involving Weierstrass functions





http://functions.wolfram.com/09.06.27.0008.01









  


  








Input Form





EllipticThetaPrime[2, z, q]/EllipticTheta[2, z, q] == ((2 Subscript[\[Omega], 1])/Pi) WeierstrassZeta[ ((2 Subscript[\[Omega], 1])/Pi) (z + Pi/2), {Subscript[g, 2], Subscript[g, 3]}] - (2 Subscript[\[Omega], 1] Subscript[\[Eta], 1])/ Pi - (4 Subscript[\[Omega], 1] Subscript[\[Eta], 1] z)/Pi^2 /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Eta], 1] == WeierstrassZeta[Subscript[\[Omega], 1], {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", "[", FractionBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]], ")"]], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["z", "+", FractionBox["\[Pi]", "2"]]], ")"]]]], "\[Pi]"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "\[Pi]"], "-", FractionBox[RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"], " ", SubscriptBox["\[Eta]", "1"]]], "\[Pi]"], "-", FractionBox[RowBox[List["4", " ", SubscriptBox["\[Omega]", "1"], " ", SubscriptBox["\[Eta]", "1"], " ", "z"]], SuperscriptBox["\[Pi]", "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["\[Eta]", "1"], "\[Equal]", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]]]]]


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





2001-10-29