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http://functions.wolfram.com/07.33.03.0601.01
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HypergeometricU[7/2, -(11/2), z] ==
(1/348364800)
(-2 Sqrt[z] (-155925 +
8 z (18900 + z (-12285 + 4 z (1755 +
2 z (-525 + 2 z (210 + z (249 + 2 z (22 + z)))))))) +
E^z Sqrt[Pi] (155925 + 2 z (-127575 +
8 z (14175 + 2 z (-4725 + z (2835 + 2 z (-945 + 4 z (315 +
z (270 + z (45 + 2 z))))))))) Erfc[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox["7", "2"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "348364800"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["18900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12285"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1755", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "525"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["210", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["249", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["22", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["155925", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "127575"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["14175", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4725"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "945"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["270", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45", "+", RowBox[List["2", " ", "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> 7 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 348364800 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </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> 45 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 270 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 315 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 945 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2835 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 4725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 127575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfc </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <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> <mn> 2 </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> <mi> z </mi> <mo> + </mo> <mn> 22 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 249 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 210 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 525 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1755 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 12285 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 18900 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='rational'> 7 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 348364800 </cn> <apply> <plus /> <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'> 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'> 45 </cn> </apply> </apply> <cn type='integer'> 270 </cn> </apply> </apply> <cn type='integer'> 315 </cn> </apply> </apply> <cn type='integer'> -945 </cn> </apply> </apply> <cn type='integer'> 2835 </cn> </apply> </apply> <cn type='integer'> -4725 </cn> </apply> </apply> <cn type='integer'> 14175 </cn> </apply> </apply> <cn type='integer'> -127575 </cn> </apply> </apply> <cn type='integer'> 155925 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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'> 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 /> <cn type='integer'> 2 </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 /> <ci> z </ci> <cn type='integer'> 22 </cn> </apply> </apply> <cn type='integer'> 249 </cn> </apply> </apply> <cn type='integer'> 210 </cn> </apply> </apply> <cn type='integer'> -525 </cn> </apply> </apply> <cn type='integer'> 1755 </cn> </apply> </apply> <cn type='integer'> -12285 </cn> </apply> </apply> <cn type='integer'> 18900 </cn> </apply> </apply> <cn type='integer'> -155925 </cn> </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["7", "2"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["18900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12285"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1755", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "525"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["210", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["249", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["22", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["155925", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "127575"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["14175", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4725"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["2835", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "945"]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["270", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["45", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], "348364800"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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