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/03.19.03.0009.01

 Input Form

 KelvinKei[-(8/3), z] == -((-1)^(3/4) Pi (-90 3^(1/3) z^(7/3) ((-I + Sqrt[3]) z^(2/3) - 2 ((-1)^(1/4) z)^(2/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 90 3^(1/3) z^(7/3) ((I + Sqrt[3]) z^(2/3) + 2^(2/3) ((1 + I) z)^(2/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 3 ((1 + I) z)^(4/3) (40 I 2^(2/3) z^(1/3) + 9 2^(2/3) z^(7/3) + (40 + 40 I) (-1)^(5/6) ((1 + I) z)^(1/3) + 9 (-1)^(1/3) z ((1 + I) z)^(4/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 3 ((1 + I) z)^(2/3) (-80 (-1)^(2/3) z + 18 (-1)^(1/6) z^3 - 40 I 2^(2/3) z^(1/3) ((1 + I) z)^(2/3) + 9 2^(2/3) z^(7/3) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 30 3^(1/3) ((3 - I Sqrt[3]) z^3 + 2^(2/3) Sqrt[3] z^(7/3) ((1 + I) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 30 3^(1/3) z^(1/3) ((-3 - I Sqrt[3]) z^(8/3) + 2^(2/3) Sqrt[3] z^2 ((1 + I) z)^(2/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(4/3)) (2 Sqrt[3] z^(7/3) (80 (-1)^(5/6) z^(2/3) + 18 (-1)^(1/3) z^(8/3) - 40 2^(2/3) ((1 + I) z)^(2/3) + (9 ((1 + I) z)^(8/3))/2^(1/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/((1 + I) z)^(4/3)) (2 Sqrt[3] z^(7/3) (-80 (-1)^(1/6) z^(2/3) - 18 (-1)^(2/3) z^(8/3) + 40 2^(2/3) ((1 + I) z)^(2/3) + (9 ((1 + I) z)^(8/3))/2^(1/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])))/ (54 2^(5/6) 3^(1/6) z^(8/3) ((1 + I) z)^(5/3))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List["-", FractionBox["8", "3"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "90"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["90", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["40", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["40", "+", RowBox[List["40", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "80"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], "+", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["40", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "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["9", " ", SuperscriptBox["2", RowBox[List["2", "/", "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["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["30", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", 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["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["30", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SqrtBox["3"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]]], RowBox[List["(", RowBox[List["2", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["80", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "-", RowBox[List["40", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]]]], SuperscriptBox["2", RowBox[List["1", "/", "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[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]]], RowBox[List["(", RowBox[List["2", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "80"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["40", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]]]], SuperscriptBox["2", RowBox[List["1", "/", "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["54", " ", SuperscriptBox["2", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 kei - 8 3 ( z ) - ( - 1 ) 3 / 4 π 54 2 5 / 6 3 6 z 8 / 3 ( ( 1 + ) z ) 5 / 3 ( - 30 3 3 ( 2 2 / 3 3 z 2 ( ( 1 + ) z ) 2 / 3 + ( - 3 - 3 ) z 8 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 - 90 3 3 ( ( + 3 ) z 2 / 3 + 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 7 / 3 - 90 3 3 ( ( - + 3 ) z 2 / 3 - 2 ( - 1 4 z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 7 / 3 + 3 ( ( 1 + ) z ) 2 / 3 ( - 40 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 + 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 18 - 1 6 z 3 - 80 ( - 1 ) 2 / 3 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 ( ( 1 + ) z ) 4 / 3 ( 40 2 2 / 3 z 3 + 9 2 2 / 3 z 7 / 3 + 9 - 1 3 ( ( 1 + ) z ) 4 / 3 z + ( - 1 ) 5 / 6 ( 40 + 40 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 30 3 3 ( 2 2 / 3 3 z 7 / 3 ( ( 1 + ) z ) 2 / 3 + ( 3 - 3 ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 ( ( 1 + ) z ) 4 / 3 2 3 z 7 / 3 ( - 80 - 1 6 z 2 / 3 - 18 ( - 1 ) 2 / 3 z 8 / 3 + 40 2 2 / 3 ( ( 1 + ) z ) 2 / 3 + 9 ( ( 1 + ) z ) 8 / 3 2 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 ( ( 1 + ) z ) 4 / 3 2 3 z 7 / 3 ( 80 ( - 1 ) 5 / 6 z 2 / 3 + 18 - 1 3 z 8 / 3 - 40 2 2 / 3 ( ( 1 + ) z ) 2 / 3 + 9 ( ( 1 + ) z ) 8 / 3 2 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei -1 8 3 z -1 -1 3 4 54 2 5 6 3 1 6 z 8 3 1 z 5 3 -1 -30 3 1 3 2 2 3 3 1 2 z 2 1 z 2 3 -3 -1 3 1 2 z 8 3 AiryBi 1 2 3 2 3 1 z 2 3 z 1 3 -1 90 3 1 3 3 1 2 z 2 3 2 2 3 1 z 2 3 AiryAi 1 2 3 2 3 1 z 2 3 z 7 3 -1 90 3 1 3 -1 3 1 2 z 2 3 -1 2 -1 1 4 z 2 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 7 3 3 1 z 2 3 -40 2 2 3 1 z 2 3 z 1 3 9 2 2 3 1 z 2 3 z 7 3 18 -1 1 6 z 3 -1 80 -1 2 3 z AiryAiPrime 1 2 3 2 3 1 z 2 3 3 1 z 4 3 40 2 2 3 z 1 3 9 2 2 3 z 7 3 9 -1 1 3 1 z 4 3 z -1 5 6 40 40 1 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 30 3 1 3 2 2 3 3 1 2 z 7 3 1 z 2 3 3 -1 3 1 2 z 3 AiryBi -1 1 2 3 2 3 1 z 2 3 1 1 z 4 3 -1 2 3 1 2 z 7 3 -80 -1 1 6 z 2 3 -1 18 -1 2 3 z 8 3 40 2 2 3 1 z 2 3 9 1 z 8 3 2 1 3 -1 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 1 z 4 3 -1 2 3 1 2 z 7 3 80 -1 5 6 z 2 3 18 -1 1 3 z 8 3 -1 40 2 2 3 1 z 2 3 9 1 z 8 3 2 1 3 -1 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[RowBox[List["-", FractionBox["8", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "90"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["90", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["40", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["40", "+", RowBox[List["40", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "80"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], "+", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["40", " ", "\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List["2", "/", "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["9", " ", SuperscriptBox["2", RowBox[List["2", "/", "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["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["30", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", 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["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["30", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SqrtBox["3"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "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"]]]]], "]"]]]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["80", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "-", RowBox[List["40", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]]]], SuperscriptBox["2", RowBox[List["1", "/", "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"]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "80"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "-", RowBox[List["18", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]]]], "+", RowBox[List["40", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["8", "/", "3"]]]]], SuperscriptBox["2", RowBox[List["1", "/", "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"]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["4", "/", "3"]]]]]], ")"]]]], RowBox[List["54", " ", SuperscriptBox["2", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["8", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "3"]]]]]]]]]]]]

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

 2007-05-02