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/03.19.03.0006.01

 Input Form

 KelvinKei[-(11/3), z] == -(Pi (18 3^(1/3) z^(7/3) (160 I + 9 z^2) ((-(-I + Sqrt[3])) z^(2/3) + 2 ((-1)^(1/4) z)^(2/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 9 3^(1/3) z ((1 + I) z)^(5/3) (-160 I + 9 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)] + 120 I ((1 + I) z)^(2/3) (-64 (-1)^(1/3) z + 18 (-1)^(5/6) z^3 + 32 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)] - 120 ((1 + I) z)^(2/3) (-64 (-1)^(2/3) z + 18 (-1)^(1/6) z^3 - 32 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)] + (1/((1 + I) z)^(1/3)) (6 3^(1/3) z^3 (160 I + 9 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)]) + 3 3^(1/3) z ((1 + I) z)^(5/3) (-160 I + 9 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)] + 40 Sqrt[3] z^(1/3) ((1 + I) z)^(2/3) (64 (-1)^(5/6) z^(2/3) + 18 (-1)^(1/3) z^(8/3) - 32 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)] + 40 Sqrt[3] z^(1/3) ((1 + I) z)^(2/3) (-64 (-1)^(2/3) z^(2/3) + 18 (-1)^(1/6) z^(8/3) + 32 I 2^(2/3) ((1 + I) z)^(2/3) - 9 2^(2/3) z^2 ((1 + I) z)^(2/3)) AiryBiPrime[ (1/2) 3^(2/3) ((1 + I) z)^(2/3)]))/(324 2^(5/6) 3^(1/6) z^(11/3) ((1 + I) z)^(5/3))

 Standard Form

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")"]]]], ")"]]]], "/", RowBox[List["(", RowBox[List["324", " ", SuperscriptBox["2", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["11", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "3"]]]]], ")"]]]]]]]]

 MathML Form

 kei - 11 3 ( z ) - π 324 2 5 / 6 3 6 z 11 / 3 ( ( 1 + ) z ) 5 / 3 ( 40 3 ( ( 1 + ) z ) 2 / 3 ( - 64 ( - 1 ) 2 / 3 z 2 / 3 + 18 - 1 6 z 8 / 3 - 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 + 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 40 3 ( 64 ( - 1 ) 5 / 6 z 2 / 3 + 18 - 1 3 z 8 / 3 - 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 + 9 ( ( 1 + ) z ) 8 / 3 2 3 ) ( ( 1 + ) z ) 2 / 3 Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 18 3 3 ( 9 z 2 + 160 ) ( 2 ( - 1 4 z ) 2 / 3 - ( - + 3 ) z 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 7 / 3 + 9 3 3 ( ( 1 + ) z ) 5 / 3 ( 9 z 2 - 160 ) ( 2 2 / 3 ( 1 + ) z 3 + ( + 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z + 3 3 3 ( ( 1 + ) z ) 5 / 3 ( 9 z 2 - 160 ) ( 2 2 / 3 3 ( 1 + ) z 3 + ( - 3 - 3 ) ( 1 + ) z 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z - 120 ( ( 1 + ) z ) 2 / 3 ( - 32 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 - 64 ( - 1 ) 2 / 3 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 120 ( ( 1 + ) z ) 2 / 3 ( 32 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 + 9 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 18 ( - 1 ) 5 / 6 z 3 - 64 - 1 3 z ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 6 3 3 z 3 ( 9 z 2 + 160 ) ( 2 2 / 3 3 ( 1 + ) z 3 + ( 3 - 3 ) ( 1 + ) z 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( 1 + ) z 3 ) KelvinKei -1 11 3 z -1 324 2 5 6 3 1 6 z 11 3 1 z 5 3 -1 40 3 1 2 1 z 2 3 -64 -1 2 3 z 2 3 18 -1 1 6 z 8 3 -1 9 2 2 3 1 z 2 3 z 2 32 2 2 3 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 z 1 3 40 3 1 2 64 -1 5 6 z 2 3 18 -1 1 3 z 8 3 -1 32 2 2 3 1 z 2 3 9 1 z 8 3 2 1 3 -1 1 z 2 3 AiryBiPrime -1 1 2 3 2 3 1 z 2 3 z 1 3 18 3 1 3 9 z 2 160 2 -1 1 4 z 2 3 -1 -1 3 1 2 z 2 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 7 3 9 3 1 3 1 z 5 3 9 z 2 -1 160 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 3 3 1 3 1 z 5 3 9 z 2 -1 160 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 -1 120 1 z 2 3 -32 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 64 -1 2 3 z AiryAiPrime 1 2 3 2 3 1 z 2 3 120 1 z 2 3 32 2 2 3 1 z 2 3 z 1 3 9 2 2 3 1 z 2 3 z 7 3 18 -1 5 6 z 3 -1 64 -1 1 3 z AiryAiPrime -1 1 2 3 2 3 1 z 2 3 6 3 1 3 z 3 9 z 2 160 2 2 3 3 1 2 1 z 1 3 3 -1 3 1 2 1 z 1 3 AiryBi -1 1 2 3 2 3 1 z 2 3 1 z 1 3 -1 [/itex]

 Rule Form

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

 2007-05-02