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/03.19.03.0011.01

 Input Form

 KelvinKei[-(7/3), z] == (1/(18 2^(2/3) 3^(1/3))) ((-1)^(1/4) Pi z^(7/3) (-((1/z^5) ((-1)^(1/6) Sqrt[3] (16 I z^(1/3) + 9 z^(7/3) - 16 (-1)^(1/12) ((-1)^(1/4) z)^(1/3) + 9 (-1)^(1/3) z ((-1)^(1/4) z)^(4/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)])) + Sqrt[3] (-16 - 9 I z^2) ((-1)^(5/6)/z^(14/3) + 1/((-1)^(1/4) z)^(14/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/(z^(14/3) ((-1)^(1/4) z)^(2/3))) (24 I 3^(1/6) ((1 + I) z)^(2/3) (z^(2/3) - (-1)^(1/6) ((-1)^(1/4) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) - (1/(z^(14/3) ((-1)^(1/4) z)^(2/3))) (24 3^(1/6) ((1 + I) z)^(2/3) (z^(2/3) - (-1)^(5/6) ((-1)^(1/4) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (-1)^(1/6) (-16 I - 9 z^2) (1/z^(14/3) + (-1)^(5/6)/((-1)^(1/4) z)^(14/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (-16 - 9 I z^2) ((-1)^(5/6)/z^(14/3) - 1/((-1)^(1/4) z)^(14/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - (1/(z^(14/3) ((-1)^(1/4) z)^(2/3))) (8 I 3^(2/3) ((1 + I) z)^(2/3) (z^(2/3) + (-1)^(1/6) ((-1)^(1/4) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(z^(14/3) ((-1)^(1/4) z)^(2/3))) (8 3^(2/3) ((1 + I) z)^(2/3) (z^(2/3) + (-1)^(5/6) ((-1)^(1/4) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])))

 Standard Form

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"z"]], ")"]], RowBox[List["14", "/", "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[RowBox[List["-", "16"]], "-", RowBox[List["9", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], SuperscriptBox["z", RowBox[List["14", "/", "3"]]]], "-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["14", "/", "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", RowBox[List[SuperscriptBox["z", RowBox[List["14", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]], RowBox[List["8", " ", "\[ImaginaryI]", " ", 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[SuperscriptBox["z", RowBox[List["2", "/", "3"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "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[FractionBox["1", RowBox[List[SuperscriptBox["z", RowBox[List["14", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]]], RowBox[List["8", " ", 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[SuperscriptBox["z", RowBox[List["2", "/", "3"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "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"]]]]], "]"]]]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 kei - 7 3 ( z ) - 1 4 π z 7 / 3 18 2 2 / 3 3 3 ( 24 3 6 ( z 2 / 3 - - 1 6 ( - 1 4 z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 z 14 / 3 ( - 1 4 z ) 2 / 3 + 8 3 2 / 3 ( z 2 / 3 + ( - 1 ) 5 / 6 ( - 1 4 z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 z 14 / 3 ( - 1 4 z ) 2 / 3 - 24 3 6 ( z 2 / 3 - ( - 1 ) 5 / 6 ( - 1 4 z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 z 14 / 3 ( - 1 4 z ) 2 / 3 - 8 3 2 / 3 ( z 2 / 3 + - 1 6 ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 z 14 / 3 ( - 1 4 z ) 2 / 3 + 3 ( - 9 z 2 - 16 ) ( 1 ( - 1 4 z ) 14 / 3 + ( - 1 ) 5 / 6 z 14 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) - 1 z 5 - 1 6 3 ( 16 z 3 + 9 z 7 / 3 + 9 - 1 3 ( - 1 4 z ) 4 / 3 z - 16 - 1 12 - 1 4 z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + ( - 9 z 2 - 16 ) ( ( - 1 ) 5 / 6 z 14 / 3 - 1 ( - 1 4 z ) 14 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + - 1 6 ( - 9 z 2 - 16 ) ( ( - 1 ) 5 / 6 ( - 1 4 z ) 14 / 3 + 1 z 14 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei -1 7 3 z -1 1 4 z 7 3 18 2 2 3 3 1 3 -1 24 3 1 6 z 2 3 -1 -1 1 6 -1 1 4 z 2 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 z 14 3 -1 1 4 z 2 3 -1 8 3 2 3 z 2 3 -1 5 6 -1 1 4 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 z 2 3 z 14 3 -1 1 4 z 2 3 -1 -1 24 3 1 6 z 2 3 -1 -1 5 6 -1 1 4 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 1 z 2 3 z 14 3 -1 1 4 z 2 3 -1 -1 8 3 2 3 z 2 3 -1 1 6 -1 1 4 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 z 14 3 -1 1 4 z 2 3 -1 3 1 2 -9 z 2 -16 1 -1 1 4 z 14 3 -1 -1 5 6 z 14 3 -1 AiryAi 1 2 3 2 3 1 z 2 3 -1 1 z 5 -1 -1 1 6 3 1 2 16 z 1 3 9 z 7 3 9 -1 1 3 -1 1 4 z 4 3 z -1 16 -1 1 12 -1 1 4 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 -9 z 2 -16 -1 5 6 z 14 3 -1 -1 1 -1 1 4 z 14 3 -1 AiryBi 1 2 3 2 3 1 z 2 3 -1 1 6 -9 z 2 -1 16 -1 5 6 -1 1 4 z 14 3 -1 1 z 14 3 -1 AiryBi -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["7", "3"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "6"]]], " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["7", "/", "3"]]]]], "-", RowBox[List["16", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "12"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02