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http://functions.wolfram.com/07.45.13.0012.01
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Wronskian[s^z WhittakerW[\[Nu], \[Mu], a r^z],
s^z WhittakerM[\[Nu], \[Mu], a r^z], z] ==
(1/2) s^(2 z) Log[r] ((1 + 2 \[Mu] + 2 \[Nu]) WhittakerM[1 + \[Nu], \[Mu],
a r^z] WhittakerW[\[Nu], \[Mu], a r^z] +
2 WhittakerM[\[Nu], \[Mu], a r^z] WhittakerW[1 + \[Nu], \[Mu], a r^z])
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["WhittakerM", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], " ", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]]]], ")"]]]]]]]]
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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> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerM] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <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> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox["M", WhittakerW] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> s </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> μ </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox["M", WhittakerM] </annotation> </semantics> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox["M", WhittakerM] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </annotation> </semantics> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <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> <apply> <ci> Subscript </ci> <apply> <ci> WhittakerM </ci> <ci> W </ci> </apply> <ci> ν </ci> <ci> μ </ci> </apply> <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> <apply> <ci> Subscript </ci> <apply> <ci> WhittakerW </ci> <ci> M </ci> </apply> <ci> ν </ci> <ci> μ </ci> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> μ </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> WhittakerM </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <ci> μ </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> WhittakerW </ci> <ci> ν </ci> <ci> μ </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> WhittakerM </ci> <ci> ν </ci> <ci> μ </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> WhittakerW </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <ci> μ </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </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["WhittakerW", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["WhittakerM", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], " ", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
