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http://functions.wolfram.com/09.32.27.0022.01
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JacobiND[z, m] == 1/(Sqrt[1 - m] JacobiSN[EllipticK[1 - m] - I EllipticK[m] -
I z, 1 - m])
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Cell[BoxData[RowBox[List[RowBox[List["JacobiND", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List["1", "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", "m"]]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], ",", RowBox[List["1", "-", "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> nd </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ❘ </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiND </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> JacobiSN </ci> <apply> <plus /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiND", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List[SqrtBox[RowBox[List["1", "-", "m"]]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], ",", RowBox[List["1", "-", "m"]]]], "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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