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EllipticK






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Representations through more general functions > Through other functions > Involving some elliptic-type functions





http://functions.wolfram.com/08.02.26.0137.01









  


  










Input Form





EllipticK[InverseEllipticNomeQ[E^((I Pi Subscript[\[Omega], 2])/ Subscript[\[Omega], 1])]] == Sqrt[Subscript[e, 1] - Subscript[e, 3]] Subscript[\[Omega], 1] /; {Subscript[e, 1], Subscript[e, 2], Subscript[e, 3]} == {WeierstrassP[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassP[Subscript[\[Omega], 1] + Subscript[\[Omega], 2], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassP[ Subscript[\[Omega], 2], {Subscript[g, 2], Subscript[g, 3]}]} && {Subscript[g, 2], Subscript[g, 3]} == WeierstrassInvariants[ {Subscript[\[Omega], 1], Subscript[\[Omega], 2]}]










Standard Form





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MathML Form







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</mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 2 </mn> </msub> </mrow> <mo fontweight='normal' fontstyle='normal'> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi fontweight='normal' fontstyle='italic'> g </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo fontweight='normal' fontstyle='italic'> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 2 </mn> </msub> </mrow> <mo fontweight='normal' fontstyle='normal'> ) </mo> </mrow> </mrow> </mrow> <mo fontweight='normal' fontstyle='normal'> } </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", SubscriptBox["\[Omega]_", "2"]]], SubscriptBox["\[Omega]_", "1"]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox[RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]]], " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["e", "1"], ",", SubscriptBox["e", "2"], ",", SubscriptBox["e", "3"]]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], "+", SubscriptBox["\[Omega]", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "}"]]]], "&&", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "2"]]], "}"]], "]"]]]]]]]]]]]]










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





2001-10-29





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