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 AiryAiPrime

 http://functions.wolfram.com/03.07.06.0026.01

 Input Form

 AiryAiPrime[z] \[Proportional] (1/(2 Sqrt[3 Pi] (-z^3)^(7/12))) (((z^2 - (-z^3)^(2/3)) Cos[(2 Sqrt[-z^3])/3 - Pi/4] - Sqrt[3] (z^2 + (-z^3)^(2/3)) Cos[(2 Sqrt[-z^3])/3 + Pi/4]) HypergeometricPFQ[{-(1/12), 5/12, 7/12, 13/12}, {1/2}, 9/(4 z^3)] - (7/(48 Sqrt[-z^3])) ((-z^2 + (-z^3)^(2/3)) Cos[(2 Sqrt[-z^3])/3 + Pi/4] - Sqrt[3] (z^2 + (-z^3)^(2/3)) Cos[(2 Sqrt[-z^3])/3 - Pi/4]) HypergeometricPFQ[{5/12, 11/12, 13/12, 19/12}, {3/2}, 9/(4 z^3)]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["3", " ", "\[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[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], " ", ")"]], RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "-", FractionBox["\[Pi]", "4"]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "+", FractionBox["\[Pi]", "4"]]], "]"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "12"]]], ",", FractionBox["5", "12"], ",", FractionBox["7", "12"], ",", FractionBox["13", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]], "-", RowBox[List[FractionBox["7", RowBox[List["48", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], " ", ")"]], RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "+", FractionBox["\[Pi]", "4"]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "-", FractionBox["\[Pi]", "4"]]], "]"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "12"], ",", FractionBox["11", "12"], ",", FractionBox["13", "12"], ",", FractionBox["19", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 Ai ( z ) 1 2 3 π ( - z 3 ) 7 / 12 ( ( ( z 2 - ( - z 3 ) 2 / 3 ) cos ( 2 - z 3 3 - π 4 ) - 3 ( ( - z 3 ) 2 / 3 + z 2 ) cos ( 2 - z 3 3 + π 4 ) ) 4 F 1 ( - 1 12 , 5 12 , 7 12 , 13 12 ; 1 2 ; 9 4 z 3 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "12"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["13", "12"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 7 48 - z 3 ( ( ( - z 3 ) 2 / 3 - z 2 ) cos ( 2 - z 3 3 + π 4 ) - 3 ( ( - z 3 ) 2 / 3 + z 2 ) cos ( 2 - z 3 3 - π 4 ) ) 4 F 1 ( 5 12 , 11 12 , 13 12 , 19 12 ; 3 2 ; 9 4 z 3 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["11", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["13", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["19", "12"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional AiryAiPrime z 1 2 3 1 2 -1 z 3 7 12 -1 z 2 -1 -1 z 3 2 3 2 -1 z 3 1 2 3 -1 -1 4 -1 -1 3 1 2 -1 z 3 2 3 z 2 2 -1 z 3 1 2 3 -1 4 -1 HypergeometricPFQ -1 1 12 5 12 7 12 13 12 1 2 9 4 z 3 -1 -1 7 48 -1 z 3 1 2 -1 -1 z 3 2 3 -1 z 2 2 -1 z 3 1 2 3 -1 4 -1 -1 3 1 2 -1 z 3 2 3 z 2 2 -1 z 3 1 2 3 -1 -1 4 -1 HypergeometricPFQ 5 12 11 12 13 12 19 12 3 2 9 4 z 3 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "-", FractionBox["\[Pi]", "4"]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "+", FractionBox["\[Pi]", "4"]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "12"]]], ",", FractionBox["5", "12"], ",", FractionBox["7", "12"], ",", FractionBox["13", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]], "-", FractionBox[RowBox[List["7", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "+", FractionBox["\[Pi]", "4"]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]], "3"], "-", FractionBox["\[Pi]", "4"]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "12"], ",", FractionBox["11", "12"], ",", FractionBox["13", "12"], ",", FractionBox["19", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]], RowBox[List["48", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["3", " ", "\[Pi]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["7", "/", "12"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2003-08-21