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http://functions.wolfram.com/03.21.13.0006.01
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Wronskian[z^p SphericalBesselJ[\[Nu], m z^q],
z^p SphericalBesselY[\[Nu], m z^q], z] == (q z^(-1 + 2 p - q))/m
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z", "p"], RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]], ",", " ", RowBox[List[SuperscriptBox["z", "p"], RowBox[List["SphericalBesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["q", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "p"]], "-", "q"]]]]], "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> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mi> p </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> j </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> q </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> p </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> y </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> q </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> q </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mi> m </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> <ci> p </ci> </apply> <apply> <ci> SphericalBesselJ </ci> <ci> ν </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> p </ci> </apply> <apply> <ci> SphericalBesselY </ci> <ci> ν </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> q </ci> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> m </ci> <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[SuperscriptBox["z_", "p_"], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["m_", " ", SuperscriptBox["z_", "q_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "p_"], " ", RowBox[List["SphericalBesselY", "[", RowBox[List["\[Nu]_", ",", RowBox[List["m_", " ", SuperscriptBox["z_", "q_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["q", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "p"]], "-", "q"]]]]], "m"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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