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JacobiCN




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCN[z,m] > Representations through equivalent functions > With related functions > Involving Weierstrass functions





http://functions.wolfram.com/09.26.27.0024.01









  


  








Input Form





JacobiCN[z, m]^2 == (WeierstrassP[z/Sqrt[Subscript[e, 1] - Subscript[e, 3]], {Subscript[g, 2], Subscript[g, 3]}] - Subscript[e, 1])/ (WeierstrassP[z/Sqrt[Subscript[e, 1] - Subscript[e, 3]], {Subscript[g, 2], Subscript[g, 3]}] - Subscript[e, 3]) /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 3] && m == ModularLambda[Subscript[\[Omega], 3]/Subscript[\[Omega], 1]] && Subscript[e, n] == WeierstrassP[Subscript[\[Omega], n], {Subscript[g, 2], Subscript[g, 3]}] && Element[n, {1, 2, 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["JacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[FractionBox["z", SqrtBox[RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", SubscriptBox["e", "1"]]], RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[FractionBox["z", SqrtBox[RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", SubscriptBox["e", "3"]]]], "/;", 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["m", "\[Equal]", RowBox[List["ModularLambda", "[", FractionBox[SubscriptBox["\[Omega]", "3"], SubscriptBox["\[Omega]", "1"]], "]"]]]], "&&", RowBox[List[SubscriptBox["e", "n"], "\[Equal]", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "&&", RowBox[List["n", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]]]


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





2001-10-29