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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/07.33.03.0763.01









  


  








Input Form





HypergeometricU[5, 0, z] == (1/2880) (24 + z (11 + z) (14 + z (8 + z)) + E^z z (120 + z (240 + z (120 + z (20 + z)))) (CoshIntegral[z] - SinhIntegral[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", "0", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2880"], RowBox[List["(", RowBox[List["24", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["14", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8", "+", "z"]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", "z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["240", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20", "+", "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> <mn> 0 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mfrac> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <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> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 20 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 120 </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> </mrow> <mo> + </mo> <mn> 24 </mn> </mrow> <mn> 2880 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 5 </cn> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <cn type='integer'> 14 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <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'> 20 </cn> </apply> </apply> <cn type='integer'> 120 </cn> </apply> </apply> <cn type='integer'> 240 </cn> </apply> </apply> <cn type='integer'> 120 </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> <cn type='integer'> 24 </cn> </apply> <apply> <power /> <cn type='integer'> 2880 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", "0", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["24", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["11", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["14", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8", "+", "z"]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", "z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["240", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], "2880"]]]]]


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





2007-05-02