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AiryBi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Integral representations > Contour integral representations





http://functions.wolfram.com/03.06.07.0005.01









  


  










Input Form





AiryBi[z] == (Pi/3^(5/6)) ((z/(2 Pi I)) ContourIntegral[Gamma[s]/(Gamma[1/2 + s] Gamma[4/3 - s] Gamma[1/2 - s])/(z^3/9)^s, \[ScriptCapitalL]["s"]] + (3^(2/3)/(2 Pi I)) ContourIntegral[ Gamma[s]/(Gamma[1/2 + s] Gamma[2/3 - s] Gamma[1/2 - s])/(z^3/9)^s, \[ScriptCapitalL]["s"]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", SuperscriptBox["3", RowBox[List["5", "/", "6"]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["z", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " "]], RowBox[List[" ", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["4", "3"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]]]], SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]], "+", RowBox[List[FractionBox[SuperscriptBox["3", RowBox[List["2", "/", "3"]]], RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " "]], RowBox[List[" ", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["2", "3"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]]]], SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]], ")"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["z", " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["4", "3"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]], "+", FractionBox[RowBox[List[SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["2", "3"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]], SuperscriptBox["3", RowBox[List["5", "/", "6"]]]]]]]]










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





2001-10-29





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