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StruveL




Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->infinity > In exponential form ||| In exponential form





http://functions.wolfram.com/03.10.06.0040.01









  


  








Input Form





StruveL[\[Nu], z] \[Proportional] (1/Sqrt[2 Pi z]) (E^z HypergeometricPFQ[{1/2 + \[Nu], 1/2 - \[Nu]}, {}, 1/(2 z)] + I E^(-z - I Pi \[Nu]) HypergeometricPFQ[ {1/2 + \[Nu], 1/2 - \[Nu]}, {}, -(1/(2 z))]) - ((2^(1 - \[Nu]) z^(\[Nu] - 1))/(Sqrt[Pi] Gamma[1/2 + \[Nu]])) HypergeometricPFQ[{1, 1/2, 1/2 - \[Nu]}, {}, 4/z^2] /; -Pi < Arg[z] < Pi/2 && (Abs[z] -> Infinity)








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["1", RowBox[List["2", " ", "z"]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["1", RowBox[List["2", " ", "z"]]]]]]], "]"]]]]]], SqrtBox[RowBox[List["2", " ", "\[Pi]", " ", "z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["4", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]


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





2007-05-02