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; }

 KelvinKei

 http://functions.wolfram.com/03.19.03.0033.01

 Input Form

 KelvinKei[11/3, z] == ((-(1/3))^(1/6) Pi z^(19/3) ((18 + 18 I) 3^(1/3) z^2 ((-160 - 160 I) z^(1/3) - (9 - 9 I) z^(7/3) + 80 2^(1/3) (-I + Sqrt[3]) ((1 + I) z)^(1/3) - 9 (-2)^(1/3) z^2 ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (9 - 9 I) 3^(1/3) z^2 (-160 I + 9 z^2) ((1 + I) (I + Sqrt[3]) z^(1/3) + 2^(1/3) (1 + I Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - 120 I z^(1/3) (32 I + 9 z^2) ((-2^(1/3)) (-I + Sqrt[3]) z^(2/3) + 2 ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 120 z^(1/3) (32 + 9 I z^2) (2^(1/3) (1 + I Sqrt[3]) z^(2/3) + (I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryAiPrime[ (1/2) 3^(2/3) ((1 + I) z)^(2/3)] - (3 - 3 I) 3^(1/3) z^2 (160 I + 9 z^2) ((2 + 2 I) Sqrt[3] z^(1/3) + 2^(1/3) (3 - I Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (3 + 3 I) 3^(1/3) z^2 (-160 I + 9 z^2) ((1 + I) (-3 I + Sqrt[3]) z^(1/3) + I 2^(1/3) (3 I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 40 (-64 I (-2)^(1/3) Sqrt[3] z - 9 2^(1/3) (3 I + Sqrt[3]) z^3 + 64 Sqrt[3] z^(1/3) ((1 + I) z)^(2/3) - 18 I Sqrt[3] z^(7/3) ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 40 z^(1/3) (-64 (-2)^(1/3) Sqrt[3] z^(2/3) + 9 2^(1/3) (3 - I Sqrt[3]) z^(8/3) + 32 (3 + I Sqrt[3]) ((1 + I) z)^(2/3) - 9 (-3 I + Sqrt[3]) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]))/ (324 2^(1/3) ((1 + I) z)^(8/3) ((-1)^(1/4) z)^(25/3))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[FractionBox["11", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["19", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["18", "+", RowBox[List["18", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "160"]], "-", RowBox[List["160", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["9", "-", RowBox[List["9", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]]]], "+", RowBox[List["80", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["9", "-", RowBox[List["9", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "160"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "-", RowBox[List["120", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["32", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["1", "/", "3"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["32", "+", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["160", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["3", "+", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "160"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["40", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "64"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["3"], " ", "z"]], "-", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["64", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["18", " ", "\[ImaginaryI]", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["40", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "64"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["32", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["324", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["25", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 kei 11 3 ( z ) - 1 3 6 π z 19 / 3 324 2 3 ( ( 1 + ) z ) 8 / 3 ( - 1 4 z ) 25 / 3 ( 120 ( 9 z 2 + 32 ) ( 2 3 ( 1 + 3 ) z 2 / 3 + ( + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 - 120 ( 9 z 2 + 32 ) ( 2 ( ( 1 + ) z ) 2 / 3 - 2 3 ( - + 3 ) z 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 40 ( - 64 - 2 3 3 z 2 / 3 + 9 2 3 ( 3 - 3 ) z 8 / 3 - 9 ( - 3 + 3 ) ( ( 1 + ) z ) 2 / 3 z 2 + 32 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 3 3 ( 9 - 9 ) ( 9 z 2 - 160 ) ( ( + 3 ) ( 1 + ) z 3 + 2 3 ( 1 + 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 ( 18 + 18 ) ( ( - 160 - 160 ) z 3 - ( 9 - 9 ) z 7 / 3 - 9 - 2 3 ( 1 + ) z 3 z 2 + 80 2 3 ( - + 3 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 ( 3 + 3 ) ( 9 z 2 - 160 ) ( ( - 3 + 3 ) ( 1 + ) z 3 + 2 3 ( 3 + 3 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - ( 3 - 3 ) 3 3 ( 9 z 2 + 160 ) ( 3 ( 2 + 2 ) z 3 + 2 3 ( 3 - 3 ) ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 40 ( 64 3 ( ( 1 + ) z ) 2 / 3 z 3 - 18 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 - 9 2 3 ( 3 + 3 ) z 3 - 64 - 2 3 3 z ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei 11 3 z -1 1 3 1 6 z 19 3 324 2 1 3 1 z 8 3 -1 1 4 z 25 3 -1 120 9 z 2 32 2 1 3 1 3 1 2 z 2 3 3 1 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 z 1 3 -1 120 9 z 2 32 2 1 z 2 3 -1 2 1 3 -1 3 1 2 z 2 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 40 -64 -2 1 3 3 1 2 z 2 3 9 2 1 3 3 -1 3 1 2 z 8 3 -1 9 -3 3 1 2 1 z 2 3 z 2 32 3 3 1 2 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 3 1 3 9 -9 9 z 2 -1 160 3 1 2 1 z 1 3 2 1 3 1 3 1 2 1 z 1 3 AiryAi 1 2 3 2 3 1 z 2 3 z 2 3 1 3 18 18 -160 -160 z 1 3 -1 9 -9 z 7 3 -1 9 -2 1 3 1 z 1 3 z 2 80 2 1 3 -1 3 1 2 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 2 3 1 3 3 3 9 z 2 -1 160 -3 3 1 2 1 z 1 3 2 1 3 3 3 1 2 1 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 z 2 -1 3 -3 3 1 3 9 z 2 160 3 1 2 2 2 z 1 3 2 1 3 3 -1 3 1 2 1 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 2 40 64 3 1 2 1 z 2 3 z 1 3 -1 18 3 1 2 1 z 2 3 z 7 3 -1 9 2 1 3 3 3 1 2 z 3 -1 64 -2 1 3 3 1 2 z AiryBiPrime -1 1 2 3 2 3 1 z 2 3 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List[FractionBox["11", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "3"]]], ")"]], RowBox[List["1", "/", "6"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["19", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["18", "+", RowBox[List["18", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "160"]], "-", RowBox[List["160", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["9", "-", RowBox[List["9", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]]]], "+", RowBox[List["80", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["9", "-", RowBox[List["9", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "160"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "-", RowBox[List["120", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["32", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["1", "/", "3"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["32", "+", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["160", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["3", "+", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "160"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["40", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "64"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["3"], " ", "z"]], "-", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["64", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["18", " ", "\[ImaginaryI]", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["40", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "64"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "2"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["32", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "]"]]]]]], ")"]]]], RowBox[List["324", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["25", "/", "3"]]]]]]]]]]

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

 2007-05-02