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; }

 AiryBi

 http://functions.wolfram.com/03.06.06.0042.01

 Input Form

 AiryBi[z] \[Proportional] ((-1)^(1/4)/((-z^3)^(5/12) (4 Sqrt[Pi]))) ((((I + Sqrt[3]) z + (-I + Sqrt[3]) (-z^3)^(1/3))/E^((2/3) I Sqrt[-z^3]) + I E^((2/3) I Sqrt[-z^3]) ((-(-I + Sqrt[3])) z - (I + Sqrt[3]) (-z^3)^(1/3))) HypergeometricPFQ[ {1/12, 5/12, 7/12, 11/12}, {1/2}, 9/(4 z^3)] + (5/(48 Sqrt[-z^3])) ((I ((I + Sqrt[3]) z + (-I + Sqrt[3]) (-z^3)^(1/3)))/ E^((2/3) I Sqrt[-z^3]) - E^((2/3) I Sqrt[-z^3]) ((-I + Sqrt[3]) z + (I + Sqrt[3]) (-z^3)^(1/3))) HypergeometricPFQ[{7/12, 11/12, 13/12, 17/12}, {3/2}, 9/(4 z^3)]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], RowBox[List["4", " ", SqrtBox["\[Pi]"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], " ", ")"]], "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], " ", "z"]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "12"], ",", FractionBox["5", "12"], ",", FractionBox["7", "12"], ",", FractionBox["11", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["5", RowBox[List["48", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "12"], ",", FractionBox["11", "12"], ",", FractionBox["13", "12"], ",", FractionBox["17", "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

 Bi ( z ) ( - z 3 ) - 5 / 12 - 1 4 4 π ( ( - 2 3 - z 3 ( ( + 3 ) z + ( - + 3 ) - z 3 3 ) + 2 3 - z 3 ( - ( + 3 ) - z 3 3 - ( - + 3 ) z ) ) 4 F 1 ( 1 12 , 5 12 , 7 12 , 11 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[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["11", "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] + 5 48 - z 3 ( - 2 3 - z 3 ( ( - + 3 ) - z 3 3 + ( + 3 ) z ) - 2 3 - z 3 ( ( + 3 ) - z 3 3 + ( - + 3 ) z ) ) 4 F 1 ( 7 12 , 11 12 , 13 12 , 17 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["7", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["11", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["13", "12"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["17", "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 AiryBi z -1 z 3 -5 12 -1 1 4 4 1 2 -1 -1 2 3 -1 -1 z 3 1 2 3 1 2 z -1 3 1 2 -1 z 3 1 3 2 3 -1 -1 z 3 1 2 -1 3 1 2 -1 z 3 1 3 -1 -1 3 1 2 z HypergeometricPFQ 1 12 5 12 7 12 11 12 1 2 9 4 z 3 -1 5 48 -1 z 3 1 2 -1 -1 2 3 -1 -1 z 3 1 2 -1 3 1 2 -1 z 3 1 3 3 1 2 z -1 2 3 -1 -1 z 3 1 2 3 1 2 -1 z 3 1 3 -1 3 1 2 z HypergeometricPFQ 7 12 11 12 13 12 17 12 3 2 9 4 z 3 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List[RowBox[List["-", "5"]], "/", "12"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], " ", "z"]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "12"], ",", FractionBox["5", "12"], ",", FractionBox["7", "12"], ",", FractionBox["11", "12"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]]], "]"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "3"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox["z", "3"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "12"], ",", FractionBox["11", "12"], ",", FractionBox["13", "12"], ",", FractionBox["17", "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["4", " ", SqrtBox["\[Pi]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2007-05-02