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http://functions.wolfram.com/03.03.13.0004.01
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Wronskian[Sqrt[z] BesselJ[1/(2 + n), (2 Sqrt[a] z^((2 + n)/2))/(2 + n)],
Sqrt[z] BesselY[1/(2 + n), (2 Sqrt[a] z^((2 + n)/2))/(2 + n)], z] ==
(2 + n)/Pi
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", RowBox[List["2", "+", "n"]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["a"], " ", SuperscriptBox["z", FractionBox[RowBox[List["2", "+", "n"]], "2"]]]], RowBox[List["2", "+", "n"]]]]], "]"]]]], ",", RowBox[List[SqrtBox["z"], " ", RowBox[List["BesselY", "[", RowBox[List[FractionBox["1", RowBox[List["2", "+", "n"]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["a"], " ", SuperscriptBox["z", FractionBox[RowBox[List["2", "+", "n"]], "2"]]]], RowBox[List["2", "+", "n"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["2", "+", "n"]], "\[Pi]"]]]]]
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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> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <msub> <mi> J </mi> <mfrac> <mn> 1 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> </msub> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> a </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <msub> <mi> Y </mi> <mfrac> <mn> 1 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> </msub> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> a </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mi> π </mi> </mfrac> </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> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselJ </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselY </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <pi /> <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["Wronskian", "[", RowBox[List[RowBox[List[SqrtBox["z_"], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", RowBox[List["2", "+", "n_"]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["a_"], " ", SuperscriptBox["z_", FractionBox[RowBox[List["2", "+", "n_"]], "2"]]]], RowBox[List["2", "+", "n_"]]]]], "]"]]]], ",", RowBox[List[SqrtBox["z_"], " ", RowBox[List["BesselY", "[", RowBox[List[FractionBox["1", RowBox[List["2", "+", "n_"]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["a_"], " ", SuperscriptBox["z_", FractionBox[RowBox[List["2", "+", "n_"]], "2"]]]], RowBox[List["2", "+", "n_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", "+", "n"]], "\[Pi]"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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