Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











StruveL






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form > Using exponential function with branch cut-containing arguments





http://functions.wolfram.com/03.10.06.0056.01









  


  










Input Form





StruveL[\[Nu], z] \[Proportional] ((1/Sqrt[2 Pi]) z^(\[Nu] + 1) (Exp[I Sqrt[-z^2] - ((2 \[Nu] + 3)/4) Pi I] (1 + (I (-1 + 4 \[Nu]^2))/(8 Sqrt[-z^2]) + (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis]) + Exp[(-I) Sqrt[-z^2] + ((2 \[Nu] + 3)/4) Pi I] (1 - (I (-1 + 4 \[Nu]^2))/(8 Sqrt[-z^2]) + (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis])))/ (-z^2)^((3 + 2 \[Nu])/4) - ((2^(1 - \[Nu]) z^(\[Nu] - 1))/ (Sqrt[Pi] Gamma[1/2 + \[Nu]])) (1 - (-1 + 2 \[Nu])/z^2 + (3 (3 - 8 \[Nu] + 4 \[Nu]^2))/z^4 + \[Ellipsis]) /; (Abs[z] -> Infinity)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox["1", SqrtBox[RowBox[List["2", "\[Pi]"]]]], SuperscriptBox["z", RowBox[List["\[Nu]", "+", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["-", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "4"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["\[ImaginaryI]", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], "-", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], ")"]]]], "-", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], SuperscriptBox["z", "4"]], "+", "\[Ellipsis]"]], ")"]]]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mtext> </mtext> <mo> &#8733; </mo> <mrow> <mrow> <mfrac> <mrow> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mtext> </mtext> </mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msup> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mrow> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> StruveL </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> <pi /> <imaginaryi /> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> <pi /> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["\[Nu]", "+", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], ")"]]]], SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], SuperscriptBox["z", "4"]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]










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





2007-05-02





© 1998- Wolfram Research, Inc.