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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > For fixed z > For fixed z and a=3





http://functions.wolfram.com/07.33.03.0569.01









  


  








Input Form





HypergeometricU[3, -1, z] == (1/24) (-5 - z + E^z z^2 (12 + 8 z + z^2) Gamma[-2, z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["3", ",", RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "24"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "-", "z", "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["8", " ", "z"]], "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "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> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 24 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mi> z </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 24 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='integer'> -2 </cn> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='integer'> -5 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["3", ",", RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "24"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "-", "z", "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["8", " ", "z"]], "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]


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





2007-05-02