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 AiryAi

 http://functions.wolfram.com/03.05.07.0001.01

 Input Form

 AiryAi[z] == (1/Pi) Integrate[Cos[t^3/3 + z t], {t, 0, Infinity}] /; Im[z] == 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAi", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "\[Pi]"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["t", "3"], "3"], "+", RowBox[List["z", " ", "t"]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Equal]", "0"]]]]]]

 MathML Form

 Ai ( z ) 1 π 0 cos ( t 3 3 + z t ) t /; Im ( z ) 0 Condition AiryAi z 1 -1 t 0 t 3 3 -1 z t z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["t", "3"], "3"], "+", RowBox[List["z", " ", "t"]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Pi]"], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Equal]", "0"]]]]]]]]

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

 2001-10-29