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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=9/2





http://functions.wolfram.com/07.33.03.0710.01









  


  










Input Form





HypergeometricU[9/2, -(5/2), z] == (1/4233600) (2 Sqrt[z] (1575 + 4 z (-840 + z (1575 + 4 z (1536 + z (689 + 4 z (24 + z)))))) - E^z Sqrt[Pi] (-1575 + 2 z (2205 + 2 z (-2205 + 2 z (3675 + 2 z (3675 + 2 z (735 + 98 z + 4 z^2)))))) Erfc[Sqrt[z]])










Standard Form





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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> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4233600 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <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> <mn> 4 </mn> <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> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 689 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1536 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 98 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 735 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3675 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3675 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2205 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2205 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1575 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfc </mi> <mo> &#8289; </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'> 9 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4233600 </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'> 4 </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'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 24 </cn> </apply> </apply> <cn type='integer'> 689 </cn> </apply> </apply> <cn type='integer'> 1536 </cn> </apply> </apply> <cn type='integer'> 1575 </cn> </apply> </apply> <cn type='integer'> -840 </cn> </apply> </apply> <cn type='integer'> 1575 </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'> 2 </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 /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 98 </cn> <ci> z </ci> </apply> <cn type='integer'> 735 </cn> </apply> </apply> <cn type='integer'> 3675 </cn> </apply> </apply> <cn type='integer'> 3675 </cn> </apply> </apply> <cn type='integer'> -2205 </cn> </apply> </apply> <cn type='integer'> 2205 </cn> </apply> </apply> <cn type='integer'> -1575 </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>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox["9", "2"], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["1575", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1575", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1536", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["689", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["24", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1575"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2205", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2205"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["3675", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["3675", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["735", "+", RowBox[List["98", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfc", "[", SqrtBox["z"], "]"]]]]]], "4233600"]]]]]










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





2007-05-02