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/07.33.03.0834.01









  


  








Input Form





HypergeometricU[6, -(11/2), -z] == -((1/4743512148375) ((16 (Sqrt[Pi] (-z)^(13/2) (2340135 - 2 z (780045 + 4 z (-45885 + 2 z (2415 + z (-115 + 2 z))))) + 2 E^z (-311850 + z (-340200 + z (-264600 + z (-201600 + z (-181440 + z (-241920 + z (-887040 + z (701145 + 4 z (-43635 + 2 z (2359 + 2 (-57 + z) z)))))))))) + Sqrt[Pi] z^(13/2) (2340135 - 2 z (780045 + 4 z (-45885 + 2 z (2415 + z (-115 + 2 z))))) Erfi[Sqrt[z]]))/E^z))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "4743512148375"], RowBox[List["(", RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45885"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "115"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "311850"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "340200"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "264600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "201600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "181440"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "887040"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["701145", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43635"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2359", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45885"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "115"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", 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> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4743512148375 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2340135 </mn> <mo> - </mo> <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> 115 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 45885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 780045 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </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> <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> <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> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 57 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2359 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 43635 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 701145 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 887040 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 241920 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 181440 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 201600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 264600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 340200 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 311850 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2340135 </mn> <mo> - </mo> <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> 115 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 45885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 780045 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 4743512148375 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 2340135 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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'> -115 </cn> </apply> </apply> <cn type='integer'> 2415 </cn> </apply> </apply> <cn type='integer'> -45885 </cn> </apply> </apply> <cn type='integer'> 780045 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <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 /> <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 /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -57 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 2359 </cn> </apply> </apply> <cn type='integer'> -43635 </cn> </apply> </apply> <cn type='integer'> 701145 </cn> </apply> </apply> <cn type='integer'> -887040 </cn> </apply> </apply> <cn type='integer'> -241920 </cn> </apply> </apply> <cn type='integer'> -181440 </cn> </apply> </apply> <cn type='integer'> -201600 </cn> </apply> </apply> <cn type='integer'> -264600 </cn> </apply> </apply> <cn type='integer'> -340200 </cn> </apply> </apply> <cn type='integer'> -311850 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 2340135 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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'> -115 </cn> </apply> </apply> <cn type='integer'> 2415 </cn> </apply> </apply> <cn type='integer'> -45885 </cn> </apply> </apply> <cn type='integer'> 780045 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </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["11", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45885"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "115"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "311850"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "340200"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "264600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "201600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "181440"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "887040"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["701145", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43635"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2359", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2340135", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["780045", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45885"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2415", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "115"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], "4743512148375"]]]]]]]


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





2007-05-02