|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/03.03.13.0010.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wronskian[z^\[Nu] BesselJ[\[Nu], m z], z^\[Nu] BesselY[\[Nu], m z], z] ==
(2 z^(2 \[Nu] - 1))/Pi
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z", "\[Nu]"], RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", "z"]]]], "]"]]]], ",", " ", RowBox[List[SuperscriptBox["z", "\[Nu]"], RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", "z"]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "1"]]]]], "\[Pi]"]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> z </mi> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> J </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> Y </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 2 </mn> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </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> z </ci> <ci> ν </ci> </apply> <apply> <ci> BesselJ </ci> <ci> ν </ci> <apply> <times /> <ci> m </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> ν </ci> </apply> <apply> <ci> BesselY </ci> <ci> ν </ci> <apply> <times /> <ci> m </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z_", "\[Nu]_"], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["m_", " ", "z_"]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "\[Nu]_"], " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", RowBox[List["m_", " ", "z_"]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "1"]]]]], "\[Pi]"]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|