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http://functions.wolfram.com/07.45.17.0002.01
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WhittakerW[\[Nu], \[Mu], z] ==
(2 + z - 2 \[Nu]) WhittakerW[\[Nu] - 1, \[Mu], z] +
((4 \[Mu]^2 - (3 - 2 \[Nu])^2)/4) WhittakerW[\[Nu] - 2, \[Mu], z]
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Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", "z", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "\[Mu]", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["\[Mu]", "2"]]], "-", SuperscriptBox[RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], "2"]]], "4"], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["\[Nu]", "-", "2"]], ",", "\[Mu]", ",", "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> <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> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </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> 2 </mn> </mrow> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </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> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WhittakerW </ci> <ci> ν </ci> <ci> μ </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> WhittakerW </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> <ci> μ </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> WhittakerW </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <ci> μ </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", "z", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "\[Mu]", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["\[Mu]", "2"]]], "-", SuperscriptBox[RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], "2"]]], ")"]], " ", RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["\[Nu]", "-", "2"]], ",", "\[Mu]", ",", "z"]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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