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=6





http://functions.wolfram.com/07.33.03.0848.01









  


  








Input Form





HypergeometricU[6, -(1/2), z] == (1/4054050) (-2 (-960 + z (11520 + z (35595 + 8 z (2905 + 2 z (342 + z (32 + z)))))) + E^z Sqrt[Pi] z^(3/2) (45045 + 2 z (45045 + 4 z (6435 + 2 z (715 + z (65 + 2 z))))) Erfc[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "4054050"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35595", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["2905", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["32", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["6435", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["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> 6 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4054050 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 65 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 715 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6435 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45045 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45045 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 32 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 342 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2905 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 35595 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11520 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 960 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4054050 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 65 </cn> </apply> </apply> <cn type='integer'> 715 </cn> </apply> </apply> <cn type='integer'> 6435 </cn> </apply> </apply> <cn type='integer'> 45045 </cn> </apply> </apply> <cn type='integer'> 45045 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 32 </cn> </apply> </apply> <cn type='integer'> 342 </cn> </apply> </apply> <cn type='integer'> 2905 </cn> </apply> </apply> <cn type='integer'> 35595 </cn> </apply> </apply> <cn type='integer'> 11520 </cn> </apply> </apply> <cn type='integer'> -960 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35595", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["2905", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["32", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["45045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["6435", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["65", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], "4054050"]]]]]


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





2007-05-02