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http://functions.wolfram.com/09.36.06.0006.01
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JacobiSN[z, m] \[Proportional] z - ((1 + m)/6) z^3 +
((1 + 14 m + m^2) z^5)/120 + \[Ellipsis] /; (z -> 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List["z", "-", RowBox[List[FractionBox[RowBox[List["1", "+", "m"]], "6"], SuperscriptBox["z", "3"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["14", " ", "m"]], "+", SuperscriptBox["m", "2"]]], ")"]], " ", SuperscriptBox["z", "5"]]], "120"], "+", "\[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> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> m </mi> </mrow> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mn> 120 </mn> </mfrac> <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> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> m </ci> </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 /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 14 </cn> <ci> m </ci> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 120 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </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["JacobiSN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", "-", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["1", "+", "m"]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List[FractionBox["1", "120"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["14", " ", "m"]], "+", 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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