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/03.19.03.0030.01

 Input Form

 KelvinKei[8/3, z] == ((1 - I)/(216 2^(5/6) 3^(1/6) z^(11/3))) (-1)^(1/12) Pi (90 3^(1/3) z^2 (2^(2/3) (1 + I Sqrt[3]) z^(1/3) - (1 - I) (I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (90 - 90 I) 3^(1/3) z^2 ((1 + I) 2^(2/3) z^(1/3) + (I + Sqrt[3]) ((1 + I) z)^(1/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 3 I (-80 (I + Sqrt[3]) z + 36 (-1)^(2/3) z^3 + 40 2^(2/3) (1 + I Sqrt[3]) z^(1/3) ((1 + I) z)^(2/3) + 9 2^(2/3) (-I + Sqrt[3]) z^(7/3) ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 6 (40 (1 - I Sqrt[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 - 30 I) 3^(1/3) z^2 (2 (-1)^(7/12) 2^(1/6) Sqrt[3] z^(1/3) + (3 + I Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (30 - 30 I) 3^(1/3) z^2 ((1 + I) 2^(2/3) Sqrt[3] z^(1/3) + (-3 - I Sqrt[3]) ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - I z^(1/3) (-160 (-1)^(1/6) Sqrt[3] z^(2/3) + 36 (-1)^(2/3) Sqrt[3] z^(8/3) - 40 2^(2/3) (3 I + Sqrt[3]) ((1 + I) z)^(2/3) + (9 (3 I + Sqrt[3]) ((1 + I) z)^(8/3))/2^(1/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 2 I Sqrt[3] z^(1/3) (80 (-1)^(1/6) z^(2/3) + 18 (-1)^(2/3) z^(8/3) - 40 2^(2/3) ((1 + I) z)^(2/3) - 9 I 2^(2/3) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])

 Standard Form

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SuperscriptBox["2", RowBox[List["2", "/", "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["2", "/", "3"]]]]], "+", FractionBox[RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", 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"]]]]], "]"]]]], 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"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 8 3 ( z ) ( 1 - ) - 1 12 π 216 2 5 / 6 3 6 z 11 / 3 ( - 2 3 ( 80 - 1 6 z 2 / 3 + 18 ( - 1 ) 2 / 3 z 8 / 3 - 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 - 40 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 - ( - 160 - 1 6 3 z 2 / 3 + 36 ( - 1 ) 2 / 3 3 z 8 / 3 - 40 2 2 / 3 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 + 9 ( 3 + 3 ) ( ( 1 + ) z ) 8 / 3 2 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 3 3 ( 90 - 90 ) ( 2 2 / 3 ( 1 + ) z 3 + ( + 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 90 3 3 ( 2 2 / 3 ( 1 + 3 ) z 3 - ( 1 - ) ( + 3 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 ( 30 - 30 ) ( 2 2 / 3 3 ( 1 + ) z 3 + ( - 3 - 3 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 + 3 3 ( 30 - 30 ) ( 2 ( - 1 ) 7 / 12 2 6 3 z 3 + ( 3 + 3 ) ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 2 - 6 ( - 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 + 40 ( 1 - 3 ) z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 ( 40 2 2 / 3 ( 1 + 3 ) ( ( 1 + ) z ) 2 / 3 z 3 + 9 2 2 / 3 ( - + 3 ) ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 36 ( - 1 ) 2 / 3 z 3 - 80 ( + 3 ) z ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei 8 3 z 1 -1 -1 1 12 216 2 5 6 3 1 6 z 11 3 -1 -2 3 1 2 80 -1 1 6 z 2 3 18 -1 2 3 z 8 3 -1 9 2 2 3 1 z 2 3 z 2 -1 40 2 2 3 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 -1 -160 -1 1 6 3 1 2 z 2 3 36 -1 2 3 3 1 2 z 8 3 -1 40 2 2 3 3 3 1 2 1 z 2 3 9 3 3 1 2 1 z 8 3 2 1 3 -1 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 3 1 3 90 -90 2 2 3 1 z 1 3 3 1 2 1 z 1 3 AiryAi 1 2 3 2 3 1 z 2 3 z 2 90 3 1 3 2 2 3 1 3 1 2 z 1 3 -1 1 -1 3 1 2 1 z 1 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 2 3 1 3 30 -30 2 2 3 3 1 2 1 z 1 3 -3 -1 3 1 2 1 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 z 2 3 1 3 30 -30 2 -1 7 12 2 1 6 3 1 2 z 1 3 3 3 1 2 1 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 2 -1 6 -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 40 1 -1 3 1 2 z AiryAiPrime 1 2 3 2 3 1 z 2 3 3 40 2 2 3 1 3 1 2 1 z 2 3 z 1 3 9 2 2 3 -1 3 1 2 1 z 2 3 z 7 3 36 -1 2 3 z 3 -1 80 3 1 2 z AiryAiPrime -1 1 2 3 2 3 1 z 2 3 [/itex]

 Rule Form

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

 2007-05-02