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WhittakerW






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Specific values > Specialized values > For fixed nu, z





http://functions.wolfram.com/07.45.03.0014.01









  


  










Input Form





WhittakerW[\[Nu], -(5/2) + \[Nu], z] == (z^(-2 + \[Nu]) (12 - 14 \[Nu] + 4 \[Nu]^2 + z (6 - 4 \[Nu]) + z^2))/E^(z/2)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], "+", "\[Nu]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["12", "-", RowBox[List["14", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", SuperscriptBox["z", "2"]]], ")"]], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], "/", "2"]]]]]]]]]










MathML Form







<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[&quot;W&quot;, WhittakerW] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WhittakerW </ci> <ci> &#957; </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], "+", "\[Nu]_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["12", "-", RowBox[List["14", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", SuperscriptBox["z", "2"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "2"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02