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; }

 AiryAi

 http://functions.wolfram.com/03.05.06.0041.01

 Input Form

 AiryAi[z] \[Proportional] (1/(4 Sqrt[3 Pi])) ((1/((-z^3)^(5/12) (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))) (Sum[Pochhammer[1/12, k] Pochhammer[5/12, k] Pochhammer[7/12, k] (Pochhammer[11/12, k]/(k! Pochhammer[1/2, k])) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 n + 3)]) + (5/(48 Sqrt[2] (-z^3)^(17/12))) (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 + 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)) (Sum[Pochhammer[7/12, k] Pochhammer[11/12, k] Pochhammer[13/12, k] (Pochhammer[17/12, k]/(k! Pochhammer[3/2, k])) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 n + 3)])) /; (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAi", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["1", RowBox[List["4", " ", SqrtBox[RowBox[List["3", " ", "\[Pi]"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], RowBox[List[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[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"]]], " ", 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RowBox[List[FractionBox["17", "12"], ",", "k"]], "]"]], "/", RowBox[List["(", RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], ",", RowBox[List["{", RowBox[List["k", ",", "0", ",", "n"]], "}"]]]], "]"]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List[RowBox[List["3", "n"]], "+", "3"]]]], "]"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 Ai ( z ) 1 4 3 π ( ( - z 3 ) - 5 / 12 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 ) ) ( k = 0 n ( 1 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "12"], ")"]], "k"], Pochhammer] ( 5 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "12"], ")"]], "k"], Pochhammer] ( 7 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["7", "12"], ")"]], "k"], Pochhammer] ( 11 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["11", "12"], ")"]], "k"], Pochhammer] k ! ( 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] ( 9 4 z 3 ) k + O ( 1 z 3 n + 3 ) ) + 5 48 2 ( - z 3 ) 17 / 12 ( 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 ) ) ( k = 0 n ( 7 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["7", "12"], ")"]], "k"], Pochhammer] ( 11 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["11", "12"], ")"]], "k"], Pochhammer] ( 13 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["13", "12"], ")"]], "k"], Pochhammer] ( 17 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["17", "12"], ")"]], "k"], Pochhammer] k ! ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] ( 9 4 z 3 ) k + O ( 1 z 3 n + 3 ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) n Condition Proportional AiryAi z 1 4 3 1 2 -1 -1 z 3 -5 12 2 1 2 z 3 2 -1 -1 2 z 3 2 3 -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 -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 3 1 2 z 5 2 1 3 1 2 -1 z 3 1 2 z -1 -1 3 1 2 -1 z 3 5 6 k 0 n Pochhammer 1 12 k Pochhammer 5 12 k Pochhammer 7 12 k Pochhammer 11 12 k k Pochhammer 1 2 k -1 9 4 z 3 -1 k O 1 z 3 n 3 -1 5 48 2 1 2 -1 z 3 17 12 -1 2 z 3 2 3 -1 -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 -1 3 1 2 -1 z 3 5 6 -1 -1 2 z 3 2 3 -1 -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 3 1 2 -1 z 3 5 6 k 0 n Pochhammer 7 12 k Pochhammer 11 12 k Pochhammer 13 12 k Pochhammer 17 12 k k Pochhammer 3 2 k -1 9 4 z 3 -1 k O 1 z 3 n 3 -1 Rule z n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], " ", 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[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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" ", SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]]]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List[RowBox[List["3", " ", "n"]], "+", "3"]]]], "]"]]]], ")"]]]], RowBox[List["48", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["17", "/", "12"]]]]]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["3", " ", "\[Pi]"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2007-05-02