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http://functions.wolfram.com/11.01.13.0002.01
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Wronskian[MathieuC[a, q, z], MathieuS[a, q, z], z] ==
(-MathieuCPrime[a, q, 0]) MathieuS[a, q, 0] +
MathieuC[a, q, 0] MathieuSPrime[a, q, 0]
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", "z"]], "]"]], ",", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], " ", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], "+", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "q", ",", "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> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> Ce </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Se </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msup> <mi> Ce </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> Ce </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Se </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msup> <mi> Ce </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a_", ",", "q_", ",", "z_"]], "]"]], ",", RowBox[List["MathieuS", "[", RowBox[List["a_", ",", "q_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], " ", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], "+", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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