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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/07.45.03.0017.01









  


  








Input Form





WhittakerW[\[Nu], 1/2 + \[Nu], z] == (E^(z/2) Gamma[1 + 2 \[Nu], z])/z^\[Nu]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ",", "z"]], "]"]]]]]]]]








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> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WhittakerW </ci> <ci> &#957; </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ",", "z"]], "]"]]]]]]]]


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





2007-05-02