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 AiryBi

 http://functions.wolfram.com/03.06.06.0048.01

 Input Form

 AiryBi[z] \[Proportional] Piecewise[ {{-(I/(E^((2 z^(3/2))/3) (2 Sqrt[Pi] z^(1/4)))) + E^((2 z^(3/2))/3)/(2 Sqrt[Pi] z^(1/4)), Arg[z] <= -((2 Pi)/3)}, {-(I/(E^((2 z^(3/2))/3) (2 Sqrt[Pi] z^(1/4)))) + E^((2 z^(3/2))/3)/(Sqrt[Pi] z^(1/4)), Inequality[-((2 Pi)/3), Less, Arg[z], LessEqual, 0]}, {I/(E^((2 z^(3/2))/3) (2 Sqrt[Pi] z^(1/4))) + E^((2 z^(3/2))/3)/(Sqrt[Pi] z^(1/4)), Inequality[0, Less, Arg[z], LessEqual, (2 Pi)/3]}}, I/(E^((2 z^(3/2))/3) (2 Sqrt[Pi] z^(1/4))) + E^((2 z^(3/2))/3)/(2 Sqrt[Pi] z^(1/4))] /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 Bi ( z ) - - 2 z 3 / 2 3 2 π z 4 + 2 z 3 / 2 3 2 π z 4 arg ( z ) - 2 π 3 - - 2 z 3 / 2 3 2 π z 4 + 2 z 3 / 2 3 π z 4 - 2 π 3 < arg ( z ) 0 - 2 z 3 / 2 3 2 π z 4 + 2 z 3 / 2 3 π z 4 0 < arg ( z ) 2 π 3 - 2 z 3 / 2 3 2 π z 4 + 2 z 3 / 2 3 2 π z 4 True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional AiryBi z -1 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 z -1 2 3 -1 -1 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 2 z 3 2 3 -1 1 2 z 1 4 -1 Inequality -1 2 3 -1 z 0 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 2 z 3 2 3 -1 1 2 z 1 4 -1 Inequality 0 z 2 3 -1 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 2 z 3 2 3 -1 2 1 2 z 1 4 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]]]]]]], List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]], List[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]]], List[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]]]]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2007-05-02