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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/03.03.26.0116.01









  


  










Input Form





BesselY[\[Nu], 2 Sqrt[z]] Hypergeometric0F1[b, -z] == (-((2^(-1 + b) Gamma[b])/Sqrt[Pi])) MeijerG[{{(1 - b)/2, 1 - b/2}, {(1 - \[Nu])/2}}, {{-(\[Nu]/2), \[Nu]/2}, {(1 - \[Nu])/2, 1 - b - \[Nu]/2, 1 - b + \[Nu]/2}}, 4 z] /; !(Element[-b - \[Nu], Integers] && -b - \[Nu] >= 0) && !(Element[-b + \[Nu], Integers] && -b + \[Nu] >= 0)










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["b_", ",", RowBox[List["-", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", RowBox[List["Gamma", "[", "b", "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", RowBox[List["1", "-", FractionBox["b", "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", "-", "b", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", "b", "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]], SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]], "\[GreaterEqual]", "0"]]]], ")"]]]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "b"]], "+", "\[Nu]"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "+", "\[Nu]"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]]]]










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





2007-05-02