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variants of this functions
Hypergeometric0F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1Regularized[b,z] > Representations through more general functions > Through Meijer G > Classical cases involving Bi





http://functions.wolfram.com/07.18.26.0104.01









  


  








Input Form





AiryBi[z] Hypergeometric0F1Regularized[b, z^3/9] == ((2^(-(1/3) + b) Sqrt[Pi])/3^(1/6)) MeijerG[{{(1/6) (4 - 3 b), (1/6) (7 - 3 b)}, {1/6, 2/3}}, {{0, 1/3}, {1/6, 2/3, 1 - b, 4/3 - b}}, (4 z^3)/9] /; Inequality[-(Pi/3), Less, Arg[z], LessEqual, Pi/3]








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["AiryBi", "[", "z_", "]"]], " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b_", ",", FractionBox[SuperscriptBox["z_", "3"], "9"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], "+", "b"]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["3", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"], ",", RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["4", "3"], "-", "b"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "9"]]], "]"]]]], SuperscriptBox["3", RowBox[List["1", "/", "6"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "3"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "3"]]]]]]]]]


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





2007-05-02