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http://functions.wolfram.com/09.37.03.0002.01
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InverseJacobiCD[z, 1/2] == -EllipticF[ArcSin[z], 1/2] + EllipticK[1/2]
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Cell[BoxData[RowBox[List[RowBox[List["InverseJacobiCD", "[", RowBox[List["z", ",", FractionBox["1", "2"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], ",", FractionBox["1", "2"]]], "]"]]]], "+", RowBox[List["EllipticK", "[", FractionBox["1", "2"], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> cd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseJacobiCD </ci> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticF </ci> <apply> <arcsin /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCD", "[", RowBox[List["z_", ",", FractionBox["1", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], ",", FractionBox["1", "2"]]], "]"]]]], "+", RowBox[List["EllipticK", "[", FractionBox["1", "2"], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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