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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Integration > Indefinite integration > Involving direct function and Bessel-type functions > Involving Bessel functions > Involving Bessel J > Power arguments





http://functions.wolfram.com/03.03.21.0079.01









  


  










Input Form





Integrate[BesselJ[-\[Nu], a Sqrt[z]] BesselY[\[Nu], b Sqrt[z]], z] == (1/(a^2 - b^2)) (2 Sqrt[z] (a BesselJ[1 - \[Nu], a Sqrt[z]] BesselY[\[Nu], b Sqrt[z]] + b BesselJ[-\[Nu], a Sqrt[z]] (BesselJ[1 - \[Nu], b Sqrt[z]] + BesselJ[-1 + \[Nu], b Sqrt[z]] Cos[Pi \[Nu]]) Csc[Pi \[Nu]]))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", RowBox[List["a_", " ", SqrtBox["z_"]]]]], "]"]], " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", RowBox[List["b_", " ", SqrtBox["z_"]]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["b", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["b", " ", SqrtBox["z"]]]]], "]"]], "+", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", RowBox[List["b", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]], ")"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]










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





2001-10-29





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