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=-11/2





http://functions.wolfram.com/07.33.03.0111.01









  


  










Input Form





HypergeometricU[-(11/2), 4, -z] == (1/(256 Sqrt[Pi] z^2)) ( (z (-10395 + 8 z (363825 + z (654885 + 2 z (197745 + z (52425 + 4 z (1647 + z (95 + 2 z))))))) BesselK[0, z/2] - (41580 + z (-155925 + 8 z (72765 + z (382695 + 2 z (154125 + z (46383 + 4 z (1555 + z (93 + 2 z)))))))) BesselK[1, z/2] - (z (-10395 + 8 z (363825 + z (654885 + 2 z (197745 + z (52425 + 4 z (1647 + z (95 + 2 z))))))) BesselI[0, z/2] + (41580 + z (-155925 + 8 z (72765 + z (382695 + 2 z (154125 + z (46383 + 4 z (1555 + z (93 + 2 z)))))))) BesselI[1, z/2]) (Log[-z] - Log[z]))/E^(z/2))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "4", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["256", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10395"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["197745", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52425", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1647", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["95", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["382695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["154125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["46383", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1555", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["93", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10395"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["197745", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52425", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1647", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["95", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["382695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["154125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["46383", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1555", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["93", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["Log", "[", "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> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 4 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </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> 2 </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> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 95 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1647 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 52425 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 197745 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 654885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 363825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10395 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> K </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </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> 2 </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> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 93 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1555 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 46383 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 154125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 382695 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 72765 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 41580 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> K </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </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> 2 </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> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 95 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1647 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 52425 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 197745 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 654885 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 363825 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10395 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </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> 2 </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> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 93 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1555 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 46383 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 154125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 382695 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 72765 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 41580 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <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'> 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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 95 </cn> </apply> </apply> <cn type='integer'> 1647 </cn> </apply> </apply> <cn type='integer'> 52425 </cn> </apply> </apply> <cn type='integer'> 197745 </cn> </apply> </apply> <cn type='integer'> 654885 </cn> </apply> </apply> <cn type='integer'> 363825 </cn> </apply> </apply> <cn type='integer'> -10395 </cn> </apply> <apply> <ci> BesselK </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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'> 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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 93 </cn> </apply> </apply> <cn type='integer'> 1555 </cn> </apply> </apply> <cn type='integer'> 46383 </cn> </apply> </apply> <cn type='integer'> 154125 </cn> </apply> </apply> <cn type='integer'> 382695 </cn> </apply> </apply> <cn type='integer'> 72765 </cn> </apply> </apply> <cn type='integer'> -155925 </cn> </apply> </apply> <cn type='integer'> 41580 </cn> </apply> <apply> <ci> BesselK </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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'> 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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 95 </cn> </apply> </apply> <cn type='integer'> 1647 </cn> </apply> </apply> <cn type='integer'> 52425 </cn> </apply> </apply> <cn type='integer'> 197745 </cn> </apply> </apply> <cn type='integer'> 654885 </cn> </apply> </apply> <cn type='integer'> 363825 </cn> </apply> </apply> <cn type='integer'> -10395 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <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'> 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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 93 </cn> </apply> </apply> <cn type='integer'> 1555 </cn> </apply> </apply> <cn type='integer'> 46383 </cn> </apply> </apply> <cn type='integer'> 154125 </cn> </apply> </apply> <cn type='integer'> 382695 </cn> </apply> </apply> <cn type='integer'> 72765 </cn> </apply> </apply> <cn type='integer'> -155925 </cn> </apply> </apply> <cn type='integer'> 41580 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </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[RowBox[List["-", FractionBox["11", "2"]]], ",", "4", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10395"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["197745", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52425", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1647", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["95", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["382695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["154125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["46383", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1555", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["93", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10395"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["363825", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["654885", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["197745", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["52425", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1647", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["95", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["41580", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "155925"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["382695", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["154125", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["46383", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1555", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["93", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]]]], ")"]]]], RowBox[List["256", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "2"]]]]]]]]










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





2007-05-02