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; }

 AiryBiPrime

 http://functions.wolfram.com/03.08.06.0046.01

 Input Form

 AiryBiPrime[z] \[Proportional] (1/(4 Sqrt[2 Pi] z (-z^3)^(5/12))) ((((-(-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))) HypergeometricPFQ[ {-(1/12), 5/12, 7/12, 13/12}, {1/2}, 9/(4 z^3)] - (7/(96 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))) HypergeometricPFQ[{5/12, 11/12, 13/12, 19/12}, {3/2}, 9/(4 z^3)]) /; (Abs[z] -> Infinity)

 Standard Form

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 MathML Form

 Bi ( z ) 1 4 2 π z ( - z 3 ) 5 / 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 ) + - 1 3 ( 2 z 3 / 2 ) ( - ( 1 + 3 ) - z 3 3 z 3 / 2 - ( - 1 + 3 ) z 5 / 2 + ( 1 + 3 ) - z 3 z + ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) ) 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 96 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 ) + - 1 3 ( 2 z 3 / 2 ) ( ( 1 + 3 ) - z 3 3 z 3 / 2 + ( - 1 + 3 ) z 5 / 2 - ( 1 + 3 ) - z 3 z - ( - 1 + 3 ) ( - z 3 ) 5 / 6 ) ) 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 AiryBiPrime z 1 4 2 1 2 z -1 z 3 5 12 -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 1 3 2 z 3 2 -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 HypergeometricPFQ -1 1 12 5 12 7 12 13 12 1 2 9 4 z 3 -1 -1 7 96 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 1 3 2 z 3 2 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 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["AiryBiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", 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[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["-", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02