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/03.19.03.0008.01

 Input Form

 KelvinKei[-(10/3), z] == (-(1/(54 2^(2/3) 3^(1/3)))) (Pi z^(10/3) (16 (-1)^(1/6) Sqrt[3] (14 I + 9 z^2) (1/z^(20/3) + (-1)^(1/3)/((-1)^(1/4) z)^(20/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 16 Sqrt[3] (-14 - 9 I z^2) ((-1)^(1/3)/z^(20/3) + 1/((-1)^(1/4) z)^(20/3)) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] - (1/(z^(20/3) ((-1)^(1/4) z)^(2/3))) (3 3^(1/6) ((1 + I) z)^(2/3) (112 I z^(2/3) + 9 z^(8/3) - 112 (-1)^(2/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(2/3) ((-1)^(1/4) z)^(8/3)) AiryAiPrime[ (-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(z^(20/3) ((-1)^(1/4) z)^(2/3))) (3 3^(1/6) ((1 + I) z)^(2/3) (112 I z^(2/3) - 9 z^(8/3) + 112 (-1)^(1/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/3) ((-1)^(1/4) z)^(8/3)) AiryAiPrime[ (1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(z^(20/3) ((-1)^(1/4) z)^(2/3))) (16 (14 I z^(2/3) + 9 z^(8/3) + 14 (-1)^(2/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/6) z^2 ((-1)^(1/4) z)^(2/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + 16 (-14 - 9 I z^2) ((-1)^(1/3)/z^(20/3) - 1/((-1)^(1/4) z)^(20/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/(z^(20/3) ((-1)^(1/4) z)^(2/3))) (3^(2/3) ((1 + I) z)^(2/3) (112 I z^(2/3) + 9 z^(8/3) + 112 (-1)^(2/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/6) z^2 ((-1)^(1/4) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/(z^(20/3) ((-1)^(1/4) z)^(2/3))) (3^(2/3) ((1 + I) z)^(2/3) (-112 I z^(2/3) + 9 z^(8/3) + 112 (-1)^(1/3) ((-1)^(1/4) z)^(2/3) + 9 (-1)^(1/3) ((-1)^(1/4) z)^(8/3)) AiryBiPrime[ (1/2) 3^(2/3) ((1 + I) z)^(2/3)])))

 Standard Form

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 MathML Form

 kei - 10 3 ( z ) - π z 10 / 3 54 2 2 / 3 3 3 ( 16 3 ( - 9 z 2 - 14 ) ( 1 ( - 1 4 z ) 20 / 3 + - 1 3 z 20 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 16 - 1 6 3 ( 9 z 2 + 14 ) ( - 1 3 ( - 1 4 z ) 20 / 3 + 1 z 20 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 z 20 / 3 ( - 1 4 z ) 2 / 3 3 3 6 ( ( 1 + ) z ) 2 / 3 ( 112 z 2 / 3 - 9 z 8 / 3 + 112 - 1 3 ( - 1 4 z ) 2 / 3 + 9 - 1 3 ( - 1 4 z ) 8 / 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) - 1 z 20 / 3 ( - 1 4 z ) 2 / 3 3 3 6 ( ( 1 + ) z ) 2 / 3 ( 112 z 2 / 3 + 9 z 8 / 3 - 112 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 + 9 ( - 1 ) 2 / 3 ( - 1 4 z ) 8 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 16 ( - 9 z 2 - 14 ) ( - 1 3 z 20 / 3 - 1 ( - 1 4 z ) 20 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 16 ( 14 z 2 / 3 + 9 z 8 / 3 + 9 - 1 6 ( - 1 4 z ) 2 / 3 z 2 + 14 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 20 / 3 ( - 1 4 z ) 2 / 3 + 1 z 20 / 3 ( - 1 4 z ) 2 / 3 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ( - 112 z 2 / 3 + 9 z 8 / 3 + 112 - 1 3 ( - 1 4 z ) 2 / 3 + 9 - 1 3 ( - 1 4 z ) 8 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) + 1 z 20 / 3 ( - 1 4 z ) 2 / 3 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ( 112 z 2 / 3 + 9 z 8 / 3 + 9 - 1 6 ( - 1 4 z ) 2 / 3 z 2 + 112 ( - 1 ) 2 / 3 ( - 1 4 z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) KelvinKei -1 10 3 z -1 z 10 3 54 2 2 3 3 1 3 -1 16 3 1 2 -9 z 2 -14 1 -1 1 4 z 20 3 -1 -1 1 3 z 20 3 -1 AiryAi 1 2 3 2 3 1 z 2 3 16 -1 1 6 3 1 2 9 z 2 14 -1 1 3 -1 1 4 z 20 3 -1 1 z 20 3 -1 AiryAi -1 1 2 3 2 3 1 z 2 3 1 z 20 3 -1 1 4 z 2 3 -1 3 3 1 6 1 z 2 3 112 z 2 3 -1 9 z 8 3 112 -1 1 3 -1 1 4 z 2 3 9 -1 1 3 -1 1 4 z 8 3 AiryAiPrime 1 2 3 2 3 1 z 2 3 -1 1 z 20 3 -1 1 4 z 2 3 -1 3 3 1 6 1 z 2 3 112 z 2 3 9 z 8 3 -1 112 -1 2 3 -1 1 4 z 2 3 9 -1 2 3 -1 1 4 z 8 3 AiryAiPrime -1 1 2 3 2 3 1 z 2 3 16 -9 z 2 -14 -1 1 3 z 20 3 -1 -1 1 -1 1 4 z 20 3 -1 AiryBi 1 2 3 2 3 1 z 2 3 16 14 z 2 3 9 z 8 3 9 -1 1 6 -1 1 4 z 2 3 z 2 14 -1 2 3 -1 1 4 z 2 3 AiryBi -1 1 2 3 2 3 1 z 2 3 z 20 3 -1 1 4 z 2 3 -1 1 z 20 3 -1 1 4 z 2 3 -1 3 2 3 1 z 2 3 -112 z 2 3 9 z 8 3 112 -1 1 3 -1 1 4 z 2 3 9 -1 1 3 -1 1 4 z 8 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 1 z 20 3 -1 1 4 z 2 3 -1 3 2 3 1 z 2 3 112 z 2 3 9 z 8 3 9 -1 1 6 -1 1 4 z 2 3 z 2 112 -1 2 3 -1 1 4 z 2 3 AiryBiPrime -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