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http://functions.wolfram.com/09.36.16.0054.01
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JacobiZeta[JacobiAmplitude[u, m], m] + JacobiZeta[JacobiAmplitude[v, m], m] -
JacobiZeta[JacobiAmplitude[u + v, m], m] == (JacobiSN[v, m]/JacobiCN[v, m])
(JacobiDN[v, m] - JacobiDN[u, m] JacobiDN[u + v, m])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["u", ",", "m"]], "]"]], ",", "m"]], "]"]], "+", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["v", ",", "m"]], "]"]], ",", "m"]], "]"]], "-", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["JacobiSN", "[", RowBox[List["v", ",", "m"]], "]"]], RowBox[List["JacobiCN", "[", RowBox[List["v", ",", "m"]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["v", ",", "m"]], "]"]], "-", RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["u", ",", "m"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "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> <mrow> <mi> Ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> u </mi> <mo> + </mo> <mi> v </mi> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> u </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> cn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> u </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> u </mi> <mo> + </mo> <mi> v </mi> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <ci> v </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> u </ci> <ci> v </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <ci> u </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> JacobiSN </ci> <ci> v </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <ci> JacobiCN </ci> <ci> v </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> JacobiDN </ci> <ci> v </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> JacobiDN </ci> <ci> u </ci> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> u </ci> <ci> v </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["u_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "+", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["v_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "-", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["u_", "+", "v_"]], ",", "m_"]], "]"]], ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["JacobiSN", "[", RowBox[List["v", ",", "m"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["v", ",", "m"]], "]"]], "-", RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["u", ",", "m"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "m"]], "]"]]]]]], ")"]]]], RowBox[List["JacobiCN", "[", RowBox[List["v", ",", "m"]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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