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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Integral transforms > Hankel transforms





http://functions.wolfram.com/03.09.22.0005.01









  


  










Input Form





HankelTransform[StruveH[\[Nu], t], {t, \[Mu]}, z] == (2 Sqrt[2/Pi] z^(-2 - \[Nu]) Gamma[(1/4) (5 + 2 \[Mu] + 2 \[Nu])] HypergeometricPFQ[{1, (1/4) (5 + 2 \[Mu] + 2 \[Nu]), (1/4) (5 - 2 \[Mu] + 2 \[Nu])}, {3/2 + \[Nu], 3/2}, 1/z^2])/ (Gamma[(1/4) (-1 + 2 \[Mu] - 2 \[Nu])] Gamma[3/2 + \[Nu]]) /; Re[\[Mu] + \[Nu]] > -(5/2)










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HankelTransform", "[", RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "t_"]], "]"]], ",", RowBox[List["{", RowBox[List["t_", ",", "\[Mu]_"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[FractionBox["2", "\[Pi]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", FractionBox["3", "2"]]], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Mu]"]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", RowBox[List["\[Mu]", "+", "\[Nu]"]], "]"]], ">", RowBox[List["-", FractionBox["5", "2"]]]]]]]]]]]










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





2001-10-29