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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 hyperbolic form ||| In hyperbolic form





http://functions.wolfram.com/03.10.06.0042.01









  


  










Input Form





StruveL[\[Nu], z] \[Proportional] (Sqrt[2]/(E^(((Pi I)/4) (1 + 2 \[Nu])) (Sqrt[Pi] Sqrt[z]))) (Sinh[((Pi I)/4) (1 + 2 \[Nu]) + z] (1 + (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/ (128 z^2) + (11025 - 51664 \[Nu]^2 + 31584 \[Nu]^4 - 5376 \[Nu]^6 + 256 \[Nu]^8)/(98304 z^4) + \[Ellipsis]) + ((1 - 4 \[Nu]^2)/(8 z)) Cosh[((Pi I)/4) (1 + 2 \[Nu]) + z] (1 + (225 - 136 \[Nu]^2 + 16 \[Nu]^4)/(384 z^2) + (893025 - 656784 \[Nu]^2 + 137824 \[Nu]^4 - 10496 \[Nu]^6 + 256 \[Nu]^8)/(491520 z^4) + \[Ellipsis])) - ((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]) /; -Pi < Arg[z] < Pi/2 && (Abs[z] -> Infinity)










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <apply> <arg /> <ci> z </ci> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </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[RowBox[List["(", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["11025", "-", RowBox[List["51664", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["31584", " ", SuperscriptBox["\[Nu]", "4"]]], "-", RowBox[List["5376", " ", SuperscriptBox["\[Nu]", "6"]]], "+", RowBox[List["256", " ", SuperscriptBox["\[Nu]", "8"]]]]], RowBox[List["98304", " ", SuperscriptBox["z", "4"]]]], "+", "\[Ellipsis]"]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["225", "-", RowBox[List["136", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["384", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["893025", "-", RowBox[List["656784", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["137824", " ", SuperscriptBox["\[Nu]", "4"]]], "-", RowBox[List["10496", " ", SuperscriptBox["\[Nu]", "6"]]], "+", RowBox[List["256", " ", SuperscriptBox["\[Nu]", "8"]]]]], RowBox[List["491520", " ", SuperscriptBox["z", "4"]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["8", " ", "z"]]]]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox["z"]]]], "-", 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["-", "\[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





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