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; }

 AiryAiPrime

 http://functions.wolfram.com/03.07.06.0040.01

 Input Form

 AiryAiPrime[z] \[Proportional] (-(1/(4 Sqrt[6 Pi] (-z^3)^(7/12)))) ((((-1 + Sqrt[3]) z^2 - (-1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) + (1 + Sqrt[3]) Sqrt[z] Sqrt[-z^3] + (1 + Sqrt[3]) (-z^3)^(2/3))/ E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^2 + (-1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) - (1 + Sqrt[3]) Sqrt[z] Sqrt[-z^3] + (1 + Sqrt[3]) (-z^3)^(2/3))) (1 - 455/(4608 z^3) - 40415375/(127401984 z^6) - 6183948445675/(1761205026816 z^9) + O[1/z^12]) - (7/(48 (-z^3)^(1/2))) (((1 + Sqrt[3]) z^2 + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) + (1 - Sqrt[3]) Sqrt[z] Sqrt[-z^3] - (1 - Sqrt[3]) (-z^3)^(2/3))/ E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((1 + Sqrt[3]) z^2 - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) - (1 - Sqrt[3]) Sqrt[z] Sqrt[-z^3] - (1 - Sqrt[3]) (-z^3)^(2/3))) (1 + 13585/(13824 z^3) + 823318925/(127401984 z^6) + 189935559402875/(1761205026816 z^9) + O[1/z^12])) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", " ", SqrtBox[RowBox[List["6", " ", "\[Pi]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["7", "/", "12"]]]]]]]], RowBox[List["(", RowBox[List[RowBox[List[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", "2"]]], "-", RowBox[List[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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RowBox[List["3", "/", "2"]]]]], "3"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], " ", ")"]], SuperscriptBox["z", "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", "/", "6"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["3"]]], " ", ")"]], SqrtBox["z"], " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["3"]]], " ", ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]]]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", FractionBox["13585", RowBox[List["13824", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox["823318925", RowBox[List["127401984", " ", SuperscriptBox["z", "6"]]]], "+", FractionBox["189935559402875", 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

 Ai ( z ) - 1 4 6 π ( - z 3 ) 7 / 12 ( ( - 1 3 ( 2 z 3 / 2 ) ( - ( - 1 + 3 ) - z 3 6 z 3 / 2 + ( - 1 + 3 ) z 2 + ( 1 + 3 ) - z 3 z + ( 1 + 3 ) ( - z 3 ) 2 / 3 ) + 2 z 3 / 2 3 ( ( - 1 + 3 ) - z 3 6 z 3 / 2 + ( - 1 + 3 ) z 2 - ( 1 + 3 ) - z 3 z + ( 1 + 3 ) ( - z 3 ) 2 / 3 ) ) ( 1 - 455 4608 z 3 - 40415375 127401984 z 6 - 6183948445675 1761205026816 z 9 + O ( 1 z 12 ) ) - 7 48 - z 3 ( - 1 3 ( 2 z 3 / 2 ) ( ( 1 + 3 ) - z 3 6 z 3 / 2 + ( 1 + 3 ) z 2 + ( 1 - 3 ) - z 3 z - ( 1 - 3 ) ( - z 3 ) 2 / 3 ) + 2 z 3 / 2 3 ( - ( 1 + 3 ) - z 3 6 z 3 / 2 + ( 1 + 3 ) z 2 - ( 1 - 3 ) - z 3 z - ( 1 - 3 ) ( - z 3 ) 2 / 3 ) ) ( 1 + 13585 13824 z 3 + 823318925 127401984 z 6 + 189935559402875 1761205026816 z 9 + O ( 1 z 12 ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional AiryAiPrime z -1 1 4 6 1 2 -1 z 3 7 12 -1 -1 1 3 2 z 3 2 -1 -1 3 1 2 -1 z 3 1 6 z 3 2 -1 3 1 2 z 2 1 3 1 2 -1 z 3 1 2 z 1 2 1 3 1 2 -1 z 3 2 3 2 z 3 2 3 -1 -1 3 1 2 -1 z 3 1 6 z 3 2 -1 3 1 2 z 2 -1 1 3 1 2 -1 z 3 1 2 z 1 2 1 3 1 2 -1 z 3 2 3 1 -1 455 4608 z 3 -1 -1 40415375 127401984 z 6 -1 -1 6183948445675 1761205026816 z 9 -1 O 1 z 12 -1 -1 7 48 -1 z 3 1 2 -1 -1 1 3 2 z 3 2 1 3 1 2 -1 z 3 1 6 z 3 2 1 3 1 2 z 2 1 -1 3 1 2 -1 z 3 1 2 z 1 2 -1 1 -1 3 1 2 -1 z 3 2 3 2 z 3 2 3 -1 -1 1 3 1 2 -1 z 3 1 6 z 3 2 1 3 1 2 z 2 -1 1 -1 3 1 2 -1 z 3 1 2 z 1 2 -1 1 -1 3 1 2 -1 z 3 2 3 1 13585 13824 z 3 -1 823318925 127401984 z 6 -1 189935559402875 1761205026816 z 9 -1 O 1 z 12 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[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", "2"]]], "-", RowBox[List[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", "/", "6"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SqrtBox["z"], " ", SqrtBox[RowBox[List["-", 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RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox["455", RowBox[List["4608", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox["40415375", RowBox[List["127401984", " ", SuperscriptBox["z", "6"]]]], "-", FractionBox["6183948445675", RowBox[List["1761205026816", " ", SuperscriptBox["z", "9"]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "12"]], "]"]]]], ")"]]]], "-", FractionBox[RowBox[List["7", " ", 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["(", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02