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/07.33.03.0842.01









  


  








Input Form





HypergeometricU[6, -(5/2), z] == (1/516891375) (-4 (-3600 + z (8640 + z (-20160 + z (107520 + z (155655 + 16 z (3855 + z (617 + z (42 + z)))))))) + 2 E^z Sqrt[Pi] z^(7/2) (328185 + 2 z (182325 + 4 z (16575 + 2 z (1275 + z (85 + 2 z))))) Erfc[Sqrt[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "516891375"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8640", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "20160"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["155655", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["3855", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["617", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["42", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["328185", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["182325", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["16575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1275", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["85", "+", 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> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 516891375 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <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> 7 </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> 85 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1275 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 16575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 182325 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 328185 </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> 4 </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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16 </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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 42 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 617 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3855 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 155655 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 107520 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 20160 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8640 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3600 </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'> 5 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 516891375 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <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'> 7 <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'> 85 </cn> </apply> </apply> <cn type='integer'> 1275 </cn> </apply> </apply> <cn type='integer'> 16575 </cn> </apply> </apply> <cn type='integer'> 182325 </cn> </apply> </apply> <cn type='integer'> 328185 </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'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 42 </cn> </apply> </apply> <cn type='integer'> 617 </cn> </apply> </apply> <cn type='integer'> 3855 </cn> </apply> </apply> <cn type='integer'> 155655 </cn> </apply> </apply> <cn type='integer'> 107520 </cn> </apply> </apply> <cn type='integer'> -20160 </cn> </apply> </apply> <cn type='integer'> 8640 </cn> </apply> </apply> <cn type='integer'> -3600 </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["5", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8640", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "20160"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107520", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["155655", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["3855", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["617", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["42", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["328185", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["182325", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["16575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1275", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["85", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], "516891375"]]]]]


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





2007-05-02