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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 > Containing Bessel functions





http://functions.wolfram.com/03.10.06.0048.01









  


  








Input Form





StruveL[\[Nu], z] - (z/Sqrt[z^2]) BesselI[\[Nu], z] \[Proportional] (-((2^(1 - \[Nu]) z^(\[Nu] - 1))/(Sqrt[Pi] Gamma[1/2 + \[Nu]]))) HypergeometricPFQ[{1/2, 1/2 - \[Nu], 1}, {}, 4/z^2] /; Abs[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[RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "-", FractionBox[RowBox[List["z_", " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], SqrtBox[SuperscriptBox["z_", "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", 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[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ",", "1"]], "}"]], ",", 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["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "\[NotEqual]", FractionBox["\[Pi]", "2"]]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]


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





2007-05-02