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=5





http://functions.wolfram.com/07.33.03.0751.01









  


  








Input Form





HypergeometricU[5, -4, z] == (1/8709120) (576 + z (-720 + z (720 + z (-840 + z (1680 + z (1650 + z (398 + z (35 + z))))))) + E^z z^5 (6 + z) (504 + z (252 + z (30 + z))) (CoshIntegral[z] - SinhIntegral[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", RowBox[List["-", "4"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "8709120"], RowBox[List["(", RowBox[List["576", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "720"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1680", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1650", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["398", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["6", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["504", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["252", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "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> 5 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8709120 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <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> 30 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 252 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 504 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <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> <mi> z </mi> <mo> + </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 398 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1650 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 720 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 720 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 576 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 5 </cn> <cn type='integer'> -4 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8709120 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 30 </cn> </apply> </apply> <cn type='integer'> 252 </cn> </apply> </apply> <cn type='integer'> 504 </cn> </apply> <apply> <plus /> <apply> <ci> CoshIntegral </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> SinhIntegral </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <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 /> <ci> z </ci> <cn type='integer'> 35 </cn> </apply> </apply> <cn type='integer'> 398 </cn> </apply> </apply> <cn type='integer'> 1650 </cn> </apply> </apply> <cn type='integer'> 1680 </cn> </apply> </apply> <cn type='integer'> -840 </cn> </apply> </apply> <cn type='integer'> 720 </cn> </apply> </apply> <cn type='integer'> -720 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 576 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", RowBox[List["-", "4"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["576", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "720"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1680", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1650", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["398", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["6", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["504", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["252", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], "8709120"]]]]]


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





2007-05-02