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/03.19.03.0005.01

 Input Form

 KelvinKei[-(13/3), z] == ((-1)^(3/4) Pi (Sqrt[3] (-4480 I z^(2/3) - 3024 z^(8/3) + 81 I z^(14/3) + 4480 (-1)^(2/3) ((-1)^(1/4) z)^(2/3) + 3024 (-1)^(1/6) z^2 ((-1)^(1/4) z)^(2/3) - 81 (-1)^(2/3) z^4 ((-1)^(1/4) z)^(2/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + Sqrt[3] (4480 z^(2/3) + 3024 I z^(8/3) - 81 z^(14/3) - 4480 (-1)^(5/6) ((-1)^(1/4) z)^(2/3) + 81 (-1)^(5/6) z^4 ((-1)^(1/4) z)^(2/3) - 3024 (-1)^(5/6) ((-1)^(1/4) z)^(8/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(2/3)) (42 I 3^(1/6) z^(5/3) (80 I + 9 z^2) (2^(2/3) (I + Sqrt[3]) z^(1/3) - (2 - 2 I) ((1 + I) z)^(1/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/((1 + I) z)^(4/3)) (42 3^(1/6) z^2 (-80 I + 9 z^2) (4 z^(2/3) + 2^(2/3) (-I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/4) (4480 I + 3024 z^2 - 81 I z^4) (4 z^(2/3) + 2^(2/3) (I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(10/3)) (z^(11/3) (-4480 - 3024 I z^2 + 81 z^4) (2^(2/3) (-I + Sqrt[3]) z^(1/3) - (2 - 2 I) ((1 + I) z)^(1/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + 7 3^(1/6) ((1 + I) z)^(2/3) (80 I + 9 z^2) (4 Sqrt[3] z^(2/3) + 2^(2/3) (3 + I Sqrt[3]) ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 7 3^(1/6) ((1 + I) z)^(2/3) (80 + 9 I z^2) (4 Sqrt[3] z^(2/3) + I 2^(2/3) (3 I + Sqrt[3]) ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]))/ (162 6^(1/3) z^(13/3) ((1 + I) z)^(2/3))

 Standard Form

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RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", 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["7", " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["80", " ", "\[ImaginaryI]"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["(", 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SuperscriptBox["6", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["13", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["2", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 kei - 13 3 ( z ) ( - 1 ) 3 / 4 π 162 6 3 z 13 / 3 ( ( 1 + ) z ) 2 / 3 ( 7 3 6 ( 9 z 2 + 80 ) ( 4 3 z 2 / 3 + 2 2 / 3 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 + 7 3 6 ( 9 z 2 + 80 ) ( 4 3 z 2 / 3 + 2 2 / 3 ( 3 + 3 ) ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 + 3 ( 4480 z 2 / 3 + 3024 z 8 / 3 - 81 z 14 / 3 + 81 ( - 1 ) 5 / 6 ( - 1 4 z ) 2 / 3 z 4 - 4480 ( - 1 ) 5 / 6 ( - 1 4 z ) 2 / 3 - 3024 ( - 1 ) 5 / 6 ( - 1 4 z ) 8 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 3 ( - 4480 z 2 / 3 - 3024 z 8 / 3 + 81 z 14 / 3 - 81 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 z 4 + 3024 - 1 6 ( - 1 4 z ) 2 / 3 z 2 + 4480 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 42 3 6 z 2 ( 9 z 2 - 80 ) ( 4 z 2 / 3 + 2 2 / 3 ( - + 3 ) ( ( 1 + ) z ) 2 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 4 / 3 + 42 3 6 z 5 / 3 ( 9 z 2 + 80 ) ( 2 2 / 3 ( + 3 ) z 3 - ( 2 - 2 ) ( 1 + ) z 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( ( 1 + ) z ) 2 / 3 + 1 ( ( 1 + ) z ) 10 / 3 z 11 / 3 ( 81 z 4 - 3024 z 2 - 4480 ) ( 2 2 / 3 ( - + 3 ) z 3 - ( 2 - 2 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 4 ( - 81 z 4 + 3024 z 2 + 4480 ) ( 4 z 2 / 3 + 2 2 / 3 ( + 3 ) ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei -1 13 3 z -1 3 4 162 6 1 3 z 13 3 1 z 2 3 -1 7 3 1 6 9 z 2 80 4 3 1 2 z 2 3 2 2 3 3 3 1 2 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 z 2 3 7 3 1 6 9 z 2 80 4 3 1 2 z 2 3 2 2 3 3 3 1 2 1 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 3 1 2 4480 z 2 3 3024 z 8 3 -1 81 z 14 3 81 -1 5 6 -1 1 4 z 2 3 z 4 -1 4480 -1 5 6 -1 1 4 z 2 3 -1 3024 -1 5 6 -1 1 4 z 8 3 AiryAi 1 2 3 2 3 1 z 2 3 3 1 2 -4480 z 2 3 -1 3024 z 8 3 81 z 14 3 -1 81 -1 2 3 -1 1 4 z 2 3 z 4 3024 -1 1 6 -1 1 4 z 2 3 z 2 4480 -1 2 3 -1 1 4 z 2 3 AiryAi -1 1 2 3 2 3 1 z 2 3 42 3 1 6 z 2 9 z 2 -1 80 4 z 2 3 2 2 3 -1 3 1 2 1 z 2 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 1 z 4 3 -1 42 3 1 6 z 5 3 9 z 2 80 2 2 3 3 1 2 z 1 3 -1 2 -2 1 z 1 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 1 z 2 3 -1 1 1 z 10 3 -1 z 11 3 81 z 4 -1 3024 z 2 -4480 2 2 3 -1 3 1 2 z 1 3 -1 2 -2 1 z 1 3 AiryBi 1 2 3 2 3 1 z 2 3 1 4 -81 z 4 3024 z 2 4480 4 z 2 3 2 2 3 3 1 2 1 z 2 3 AiryBi -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