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/07.33.03.0835.01









  


  








Input Form





HypergeometricU[6, -5, z] == (1/4790016000) (14400 - z (17280 + z (-15120 + z (13440 + z (-15120 + z (30240 + z (31594 + z (8904 + z (1047 + z (54 + z))))))))) - E^z z^6 (55440 + z (39600 + z (9900 + z (1100 + z (55 + z))))) (CoshIntegral[z] - SinhIntegral[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", "5"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "4790016000"], RowBox[List["(", RowBox[List["14400", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["17280", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15120"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["13440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15120"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30240", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["31594", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8904", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1047", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["54", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["55440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["39600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1100", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["55", "+", "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> 6 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4790016000 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> </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> <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> 55 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1100 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 9900 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 39600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 55440 </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> 6 </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> <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> 54 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1047 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8904 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 31594 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 15120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 13440 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 15120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 17280 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 14400 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 6 </cn> <cn type='integer'> -5 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4790016000 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </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 /> <ci> z </ci> <cn type='integer'> 55 </cn> </apply> </apply> <cn type='integer'> 1100 </cn> </apply> </apply> <cn type='integer'> 9900 </cn> </apply> </apply> <cn type='integer'> 39600 </cn> </apply> </apply> <cn type='integer'> 55440 </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'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 54 </cn> </apply> </apply> <cn type='integer'> 1047 </cn> </apply> </apply> <cn type='integer'> 8904 </cn> </apply> </apply> <cn type='integer'> 31594 </cn> </apply> </apply> <cn type='integer'> 30240 </cn> </apply> </apply> <cn type='integer'> -15120 </cn> </apply> </apply> <cn type='integer'> 13440 </cn> </apply> </apply> <cn type='integer'> -15120 </cn> </apply> </apply> <cn type='integer'> 17280 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 14400 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", "5"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["14400", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["17280", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15120"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["13440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15120"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30240", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["31594", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8904", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1047", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["54", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["55440", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["39600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["9900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1100", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["55", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], "4790016000"]]]]]


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





2007-05-02