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http://functions.wolfram.com/09.37.06.0001.02
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InverseJacobiCD[z, m] \[Proportional] EllipticK[m] - z - ((m + 1)/6) z^3 -
((3 + 2 m + 3 m^2)/40) z^5 - \[Ellipsis] /; (z -> 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "-", "z", "-", RowBox[List[FractionBox[RowBox[List["m", "+", "1"]], "6"], SuperscriptBox["z", "3"]]], "-", RowBox[List[FractionBox[RowBox[List["3", "+", RowBox[List["2", " ", "m"]], "+", RowBox[List["3", " ", SuperscriptBox["m", "2"]]]]], "40"], SuperscriptBox["z", "5"]]], "-", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]
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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> <mrow> <msup> <mi> cd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mi> z </mi> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 3 </mn> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mn> 40 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> InverseJacobiCD </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 40 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> … </ci> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCD", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "-", "z", "-", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["m", "+", "1"]], ")"]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[FractionBox["1", "40"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "m"]], "+", RowBox[List["3", " ", SuperscriptBox["m", "2"]]]]], ")"]], " ", SuperscriptBox["z", "5"]]], "-", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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