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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integral transforms > Hankel transforms





http://functions.wolfram.com/01.06.22.0007.01









  


  










Input Form





HankelTransform[t^(\[Alpha] - 1) Sin[t], {t, \[Nu]}, z] == (-(z^(1/2 + \[Nu])/(2^\[Nu] Gamma[1 + \[Nu]]))) Cos[(1/4) Pi (3 + 2 \[Alpha] + 2 \[Nu])] Gamma[1/2 + \[Alpha] + \[Nu]] Hypergeometric2F1[(1/4) (1 + 2 \[Alpha] + 2 \[Nu]), (1/4) (3 + 2 \[Alpha] + 2 \[Nu]), 1 + \[Nu], z^2] /; Re[\[Alpha] + \[Nu]] > -(3/2) && Re[\[Alpha]] < 1










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[SuperscriptBox["t_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["Sin", "[", "t_", "]"]]]], ",", RowBox[List["{", RowBox[List["t_", ",", "\[Nu]_"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Alpha]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Alpha]", "+", "\[Nu]"]], "]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Alpha]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Alpha]"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List["1", "+", "\[Nu]"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", "\[Nu]"]], "]"]], ">", RowBox[List["-", FractionBox["3", "2"]]]]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Alpha]", "]"]], "<", "1"]]]]]]]]]]










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





2001-10-29





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