html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 AiryBi

 http://functions.wolfram.com/03.06.06.0043.01

 Input Form

 AiryBi[z] \[Proportional] (1/((-z^3)^(5/12) (8 Sqrt[Pi]))) ((Sqrt[2]/z^(3/2)) (((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) - (1 + Sqrt[3]) z Sqrt[-z^3] - (-1 + Sqrt[3]) (-z^3)^(5/6))/E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))) (1 + 385/(4608 z^3) + 37182145/(127401984 z^6) + 5849680962125/(1761205026816 z^9) + O[1/z^12]) + (5/(24 Sqrt[2] z^3)) (((-(-1 + Sqrt[3])) z^(5/2) - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))/E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))) (1 + 17017/(13824 z^3) + 1078282205/(127401984 z^6) + 253541886272675/(1761205026816 z^9) + O[1/z^12])) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], RowBox[List["8", " ", SqrtBox["\[Pi]"]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[SqrtBox["2"], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["5", "/", "6"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["5", "/", "6"]]]]]]], ")"]]]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", FractionBox["385", RowBox[List["4608", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox["37182145", RowBox[List["127401984", " ", SuperscriptBox["z", "6"]]]], "+", FractionBox["5849680962125", RowBox[List["1761205026816", " ", SuperscriptBox["z", "9"]]]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "12"]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["5", RowBox[List["24", " ", SqrtBox["2"], " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["5", "/", "6"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["5", "/", "6"]]]]]]], ")"]]]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", FractionBox["17017", RowBox[List["13824", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox["1078282205", RowBox[List["127401984", " ", SuperscriptBox["z", "6"]]]], "+", FractionBox["253541886272675", RowBox[List["1761205026816", " ", SuperscriptBox["z", "9"]]]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "12"]], "]"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 Bi ( z ) ( - z 3 ) - 5 / 12 8 π ( 2 z 3 / 2 ( 2 z 3 / 2 3 ( ( 1 + 3 ) - z 3 3 z 3 / 2 + ( - 1 + 3 ) z 5 / 2 + ( 1 + 3 ) - z 3 z + ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) + - 2 z 3 / 2 3 ( ( 1 + 3 ) - z 3 3 z 3 / 2 + ( - 1 + 3 ) z 5 / 2 - ( 1 + 3 ) - z 3 z - ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) ) ( 1 + 385 4608 z 3 + 37182145 127401984 z 6 + 5849680962125 1761205026816 z 9 + O ( 1 z 12 ) ) + 5 24 2 z 3 ( 2 z 3 / 2 3 ( ( 1 + 3 ) - z 3 3 z 3 / 2 + ( - 1 + 3 ) z 5 / 2 + ( 1 + 3 ) - z 3 z + ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) + - 2 z 3 / 2 3 ( - ( 1 + 3 ) - z 3 3 z 3 / 2 - ( - 1 + 3 ) z 5 / 2 + ( 1 + 3 ) - z 3 z + ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) ) ( 1 + 17017 13824 z 3 + 1078282205 127401984 z 6 + 253541886272675 1761205026816 z 9 + O ( 1 z 12 ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional AiryBi z -1 z 3 -5 12 8 1 2 -1 2 1 2 z 3 2 -1 2 z 3 2 3 -1 1 3 1 2 -1 z 3 1 3 z 3 2 -1 3 1 2 z 5 2 1 3 1 2 -1 z 3 1 2 z -1 3 1 2 -1 z 3 5 6 -1 2 z 3 2 3 -1 1 3 1 2 -1 z 3 1 3 z 3 2 -1 3 1 2 z 5 2 -1 1 3 1 2 -1 z 3 1 2 z -1 -1 3 1 2 -1 z 3 5 6 1 385 4608 z 3 -1 37182145 127401984 z 6 -1 5849680962125 1761205026816 z 9 -1 O 1 z 12 -1 5 24 2 1 2 z 3 -1 2 z 3 2 3 -1 1 3 1 2 -1 z 3 1 3 z 3 2 -1 3 1 2 z 5 2 1 3 1 2 -1 z 3 1 2 z -1 3 1 2 -1 z 3 5 6 -1 2 z 3 2 3 -1 -1 1 3 1 2 -1 z 3 1 3 z 3 2 -1 -1 3 1 2 z 5 2 1 3 1 2 -1 z 3 1 2 z -1 3 1 2 -1 z 3 5 6 1 17017 13824 z 3 -1 1078282205 127401984 z 6 -1 253541886272675 1761205026816 z 9 -1 O 1 z 12 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["5", "/", "6"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02