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http://functions.wolfram.com/07.33.03.0788.01
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HypergeometricU[11/2, -(9/2), z] == (1/109734912000)
(2 Sqrt[z] (893025 + 2 z (-694575 +
8 z (91665 + 2 z (-46305 + z (59535 + 2 z (83955 + 4 z (8805 +
z (1374 + z (89 + 2 z))))))))) -
E^z Sqrt[Pi] (-893025 +
4 z (496125 + z (-637875 + 8 z (85050 +
z (-99225 + 4 z (59535 + z (99225 + 2 z (18900 + z (2835 +
4 z (45 + z)))))))))) Erfc[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "109734912000"], RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["893025", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "694575"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["91665", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46305"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["83955", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["8805", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1374", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["89", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "893025"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["496125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "637875"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["85050", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "99225"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["99225", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["18900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["45", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], ")"]]]]]]]]
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<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["U", HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 109734912000 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 89 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1374 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8805 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 83955 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 59535 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 46305 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 91665 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 694575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 893025 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 45 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2835 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 18900 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 99225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 59535 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 99225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 85050 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 637875 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 496125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 893025 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfc </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='rational'> 11 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 109734912000 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <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'> 8 </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> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <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'> 89 </cn> </apply> </apply> <cn type='integer'> 1374 </cn> </apply> </apply> <cn type='integer'> 8805 </cn> </apply> </apply> <cn type='integer'> 83955 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> -46305 </cn> </apply> </apply> <cn type='integer'> 91665 </cn> </apply> </apply> <cn type='integer'> -694575 </cn> </apply> </apply> <cn type='integer'> 893025 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <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 /> <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'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 45 </cn> </apply> </apply> <cn type='integer'> 2835 </cn> </apply> </apply> <cn type='integer'> 18900 </cn> </apply> </apply> <cn type='integer'> 99225 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> -99225 </cn> </apply> </apply> <cn type='integer'> 85050 </cn> </apply> </apply> <cn type='integer'> -637875 </cn> </apply> </apply> <cn type='integer'> 496125 </cn> </apply> </apply> <cn type='integer'> -893025 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox["11", "2"], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["893025", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "694575"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["91665", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "46305"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["83955", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["8805", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1374", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["89", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "893025"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["496125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "637875"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["85050", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "99225"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["59535", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["99225", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["18900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["45", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], "109734912000"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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