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http://functions.wolfram.com/09.27.27.0021.01
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JacobiCS[z, m] == I/JacobiSN[I z, 1 - m]
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Cell[BoxData[RowBox[List[RowBox[List["JacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", FractionBox[RowBox[List["\[ImaginaryI]", " "]], RowBox[List["JacobiSN", "[", RowBox[List[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> cs </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mi> ⅈ </mi> <mrow> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <ci> JacobiSN </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </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["JacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["\[ImaginaryI]", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", RowBox[List["1", "-", "m"]]]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
