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http://functions.wolfram.com/06.32.13.0011.01
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Wronskian[s^z FresnelS[a r^z], s^z FresnelC[a r^z], s^z, z] ==
(-a^4) Pi r^(4 z) s^(3 z) Log[r]^3
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["FresnelS", "[", RowBox[List["a", " ", SuperscriptBox["r", "z"]]], "]"]]]], " ", ",", RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["FresnelC", "[", RowBox[List["a", " ", SuperscriptBox["r", "z"]]], "]"]]]], ",", SuperscriptBox["s", "z"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["a", "4"]]], " ", "\[Pi]", " ", SuperscriptBox["r", RowBox[List["4", " ", "z"]]], " ", SuperscriptBox["s", RowBox[List["3", " ", "z"]]], " ", SuperscriptBox[RowBox[List["Log", "[", "r", "]"]], "3"]]]]]]]
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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> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> S </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> C </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <msup> <mi> s </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> s </mi> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> S </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> C </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <pi /> <apply> <power /> <ci> r </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["FresnelS", "[", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["FresnelC", "[", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]], "]"]]]], ",", SuperscriptBox["s_", "z_"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["a", "4"]]], " ", "\[Pi]", " ", SuperscriptBox["r", RowBox[List["4", " ", "z"]]], " ", SuperscriptBox["s", RowBox[List["3", " ", "z"]]], " ", SuperscriptBox[RowBox[List["Log", "[", "r", "]"]], "3"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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