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http://functions.wolfram.com/09.29.27.0064.01
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JacobiDN[z, m] == (-(-1 + JacobiCN[z, m])) (1 + JacobiCN[z, m])
JacobiDS[z, m] JacobiNS[z, m]
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Cell[BoxData[RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], " ", RowBox[List["JacobiDS", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiNS", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]
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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> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> ds </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> ns </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> JacobiDS </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> JacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], " ", RowBox[List["JacobiDS", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiNS", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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