Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > For fixed z > For fixed z and a=4





http://functions.wolfram.com/07.33.03.0662.01









  


  








Input Form





HypergeometricU[4, -1, z] == (1/1440) (12 - 48 z - 94 z^2 - 28 z^3 - 2 z^4 - 2 E^z z^2 (60 + 60 z + 15 z^2 + z^3) ExpIntegralEi[-z] - E^z z^2 (60 + 60 z + 15 z^2 + z^3) Log[-(1/z)] + E^z z^2 (60 + 60 z + 15 z^2 + z^3) Log[-z] - 2 E^z z^2 (60 + 60 z + 15 z^2 + z^3) Log[z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1440"], RowBox[List["(", RowBox[List["12", "-", RowBox[List["48", " ", "z"]], "-", RowBox[List["94", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "z"]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", "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> 4 </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> 1440 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 94 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1440 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> <cn type='integer'> 60 </cn> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> <cn type='integer'> 60 </cn> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> <cn type='integer'> 60 </cn> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> <cn type='integer'> 60 </cn> </apply> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 94 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 48 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["12", "-", RowBox[List["48", " ", "z"]], "-", RowBox[List["94", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "z"]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "3"]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]]]], "1440"]]]]]


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





2007-05-02