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/07.33.03.0654.01









  


  










Input Form





HypergeometricU[4, -(7/2), z] == (1/6081075) (16 (315 + 2 z (-180 + z (180 + z (-240 + z (840 + z (543 + 4 z (22 + z)))))) - E^z Sqrt[Pi] z^(9/2) (2145 + 2 z (585 + 90 z + 4 z^2)) Erfc[Sqrt[z]]))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "6081075"], RowBox[List["(", RowBox[List["16", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["180", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["840", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["543", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["22", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", 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> 4 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6081075 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <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> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 90 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 585 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2145 </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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> <mi> z </mi> <mo> + </mo> <mn> 22 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 543 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 180 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 180 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 315 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6081075 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <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> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 90 </cn> <ci> z </ci> </apply> <cn type='integer'> 585 </cn> </apply> </apply> <cn type='integer'> 2145 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 22 </cn> </apply> </apply> <cn type='integer'> 543 </cn> </apply> </apply> <cn type='integer'> 840 </cn> </apply> </apply> <cn type='integer'> -240 </cn> </apply> </apply> <cn type='integer'> 180 </cn> </apply> </apply> <cn type='integer'> -180 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 315 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["180", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["840", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["543", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["22", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], "6081075"]]]]]










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





2007-05-02