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/03.07.06.0049.01

 Input Form

 AiryAiPrime[z] \[Proportional] (-(1/(2 Sqrt[6 Pi] (-z^3)^(7/12)))) ((((-1 + Sqrt[3]) z^2 + (1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] - Sqrt[z] (-z^3)^(1/6) ((1 - Sqrt[3]) z + (1 + Sqrt[3]) (-z^3)^(1/3)) Sinh[(2 z^(3/2))/3]) HypergeometricPFQ[{-(1/12), 5/12, 7/12, 13/12}, {1/2}, 9/(4 z^3)] - (7/(48 (-z^3)^(1/2))) (((1 + Sqrt[3]) z^2 + (-1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] + Sqrt[z] (-z^3)^(1/6) ((-(1 + Sqrt[3])) z + (-1 + Sqrt[3]) (-z^3)^(1/3)) Sinh[(2 z^(3/2))/3]) 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[RowBox[List["-", FractionBox["1", RowBox[List["2", " ", 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[RowBox[List["(", 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[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[SqrtBox["z"], SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]], 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", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "2"]]]]]], RowBox[List["(", RowBox[List[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[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "+", RowBox[List[SqrtBox["z"], SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]]]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]], 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 6 π ( - z 3 ) 7 / 12 ( ( ( ( 1 + 3 ) ( - z 3 ) 2 / 3 + ( - 1 + 3 ) z 2 ) cosh ( 2 z 3 / 2 3 ) - z - z 3 6 ( ( 1 + 3 ) - z 3 3 + ( 1 - 3 ) z ) sinh ( 2 z 3 / 2 3 ) ) 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]", "4"], SubscriptBox["F", "1"]]], "\[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 ( ( - 1 + 3 ) - z 3 3 - ( 1 + 3 ) z ) sinh ( 2 z 3 / 2 3 ) - z 3 6 + ( ( - 1 + 3 ) ( - z 3 ) 2 / 3 + ( 1 + 3 ) z 2 ) cosh ( 2 z 3 / 2 3 ) ) 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]", "4"], SubscriptBox["F", "1"]]], "\[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 1 2 6 1 2 -1 z 3 7 12 -1 1 3 1 2 -1 z 3 2 3 -1 3 1 2 z 2 2 z 3 2 3 -1 -1 z 1 2 -1 z 3 1 6 1 3 1 2 -1 z 3 1 3 1 -1 3 1 2 z 2 z 3 2 3 -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 z 1 2 -1 3 1 2 -1 z 3 1 3 -1 1 3 1 2 z 2 z 3 2 3 -1 -1 z 3 1 6 -1 3 1 2 -1 z 3 2 3 1 3 1 2 z 2 2 z 3 2 3 -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[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", 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[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[SqrtBox["z"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]], " ", 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[RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "+", RowBox[List[SqrtBox["z"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["1", "+", SqrtBox["3"]]], ")"]]]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]], " ", 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["6", " ", "\[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)

 2007-05-02