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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 0F~1





http://functions.wolfram.com/03.03.26.0138.01









  


  








Input Form





BesselY[\[Nu], 2 Sqrt[z]] Hypergeometric0F1Regularized[-\[Nu], -z] == (-(2^(-1 - \[Nu])/Pi)) (2^\[Nu] z^(\[Nu]/2) Cos[Pi \[Nu]] + Sqrt[Pi] MeijerG[{{(1 + \[Nu])/2}, {(1 - \[Nu])/2}}, {{-(\[Nu]/2), \[Nu]/2}, {(1 - \[Nu])/2, 1 + (3 \[Nu])/2}}, 4 z])








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["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", RowBox[List["-", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "+", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]]]], ")"]]]], "\[Pi]"]]]]]]]


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





2007-05-02