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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving 0F1





http://functions.wolfram.com/03.03.26.0125.01









  


  










Input Form





BesselY[\[Nu], 2 Sqrt[z]] Hypergeometric0F1[1 - \[Nu], z] == 2^(\[Nu]/2) Sqrt[Pi] Gamma[1 - \[Nu]] MeijerG[{{}, {(1/4) (-1 - \[Nu]), (1 - \[Nu])/4}}, {{(2 + \[Nu])/4, \[Nu]/4, -(\[Nu]/4)}, {(1/4) (-1 - \[Nu]), (3 \[Nu])/4, (1 - \[Nu])/4}}, z^2/4] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", RowBox[List["2", " ", SqrtBox["z_"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]_"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["\[Nu]", "/", "2"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]], ")"]]]], ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "+", "\[Nu]"]], "4"], ",", FractionBox["\[Nu]", "4"], ",", RowBox[List["-", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]], ")"]]]], ",", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"], ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "4"]]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]










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





2007-05-02