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StruveL






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/03.10.21.0013.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) StruveL[\[Nu], b t])/E^(a t), {t, 0, Infinity}] == ((a^(-1 - \[Alpha] - \[Nu]) b^(1 + \[Nu]) Gamma[1 + \[Alpha] + \[Nu]])/(2^\[Nu] (Sqrt[Pi] Gamma[3/2 + \[Nu]]))) HypergeometricPFQ[{1, (1/2) (2 + \[Alpha] + \[Nu]), (1/2) (1 + \[Alpha] + \[Nu])}, {3/2 + \[Nu], 3/2}, b^2/a^2] /; Re[\[Alpha] + \[Nu]] > -1 && Re[a] > Abs[Re[b]]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "a_"]], " ", "t_"]]], " ", RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", RowBox[List["b_", " ", "t_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["a", RowBox[List[RowBox[List["-", "1"]], "-", "\[Alpha]", "-", "\[Nu]"]]], " ", SuperscriptBox["b", RowBox[List["1", "+", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Alpha]", "+", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Alpha]", "+", "\[Nu]"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "\[Alpha]", "+", "\[Nu]"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", FractionBox["3", "2"]]], "}"]], ",", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", "\[Nu]"]], "]"]], ">", RowBox[List["-", "1"]]]], "&&", RowBox[List[RowBox[List["Re", "[", "a", "]"]], ">", RowBox[List["Abs", "[", RowBox[List["Re", "[", "b", "]"]], "]"]]]]]]]]]]]]










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





2001-10-29