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; }

 KelvinKer

 http://functions.wolfram.com/03.20.03.0003.01

 Input Form

 KelvinKer[-(14/3), z] == -((-1)^(3/4) Pi (144 I 3^(1/3) z^(1/3) (110 I + 9 z^2) ((-(-I + Sqrt[3])) z^(2/3) + 2^(2/3) ((1 + I) z)^(2/3)) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(1/3)) (144 3^(1/3) z (110 + 9 I 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)]) + (1/((1 + I) z)^(4/3)) (3 I (28160 (-1)^(1/3) z - 8640 (-1)^(5/6) z^3 - 162 (-1)^(1/3) z^5 - 14080 I 2^(2/3) z^(1/3) ((1 + I) z)^(2/3) - 4320 2^(2/3) z^(7/3) ((1 + I) z)^(2/3) + 81 I 2^(2/3) z^(13/3) ((1 + I) z)^(2/3)) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) + (1/((1 + I) z)^(4/3)) (3 (-28160 (-1)^(1/6) z - 8640 (-1)^(2/3) z^3 + 162 (-1)^(1/6) z^5 - 14080 2^(2/3) z^(1/3) ((1 + I) z)^(2/3) - 4320 I 2^(2/3) z^(7/3) ((1 + I) z)^(2/3) + 81 2^(2/3) z^(13/3) ((1 + I) z)^(2/3)) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]) + 48 3^(1/3) z^(1/3) (110 I (3 I + Sqrt[3]) z^(2/3) + 18 (-1)^(1/3) Sqrt[3] z^(8/3) - 110 2^(2/3) Sqrt[3] ((1 + I) z)^(2/3) + (9 Sqrt[3] ((1 + I) z)^(8/3))/2^(1/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/((1 + I) z)^(1/3)) (48 3^(1/3) z (110 + 9 I 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)]) - (1/((1 + I) z)^(4/3)) (Sqrt[3] z^(1/3) (28160 (-1)^(5/6) z^(2/3) + 8640 (-1)^(1/3) z^(8/3) - 162 (-1)^(5/6) z^(14/3) - 14080 2^(2/3) ((1 + I) z)^(2/3) + 4320 I 2^(2/3) z^2 ((1 + I) z)^(2/3) + 81 2^(2/3) z^4 ((1 + I) z)^(2/3)) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)]) - (1/((1 + I) z)^(4/3)) (Sqrt[3] z^(1/3) (-28160 (-1)^(1/6) z^(2/3) - 8640 (-1)^(2/3) z^(8/3) + 162 (-1)^(1/6) z^(14/3) + 14080 2^(2/3) ((1 + I) z)^(2/3) + 4320 I 2^(2/3) z^2 ((1 + I) z)^(2/3) - 81 2^(2/3) z^4 ((1 + I) z)^(2/3)) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)])))/ (243 2^(5/6) 3^(1/6) z^(8/3) ((1 + I) z)^(5/3))

 Standard Form

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 MathML Form

 ker - 14 3 ( z ) - ( - 1 ) 3 / 4 π 243 2 5 / 6 3 6 z 8 / 3 ( ( 1 + ) z ) 5 / 3 ( 144 3 3 ( 9 z 2 + 110 ) ( 2 2 / 3 ( ( 1 + ) z ) 2 / 3 - ( - + 3 ) z 2 / 3 ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 48 3 3 ( 110 ( 3 + 3 ) z 2 / 3 + 18 - 1 3 3 z 8 / 3 - 110 2 2 / 3 3 ( ( 1 + ) z ) 2 / 3 + 9 3 ( ( 1 + ) z ) 8 / 3 2 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) z 3 + 144 3 3 z ( 9 z 2 + 110 ) ( 2 2 / 3 ( 1 + ) z 3 + ( + 3 ) ( 1 + ) z 3 ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ( 1 + ) z 3 + 1 ( ( 1 + ) z ) 4 / 3 ( 3 ( - 14080 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 - 4320 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 81 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 13 / 3 + 162 - 1 6 z 5 - 8640 ( - 1 ) 2 / 3 z 3 - 28160 - 1 6 z ) Ai ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) + 1 ( ( 1 + ) z ) 4 / 3 ( 3 ( - 14080 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 3 - 4320 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 7 / 3 + 81 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 13 / 3 - 162 - 1 3 z 5 - 8640 ( - 1 ) 5 / 6 z 3 + 28160 - 1 3 z ) Ai ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) + 48 3 3 z ( 9 z 2 + 110 ) ( 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 - 1 ( ( 1 + ) z ) 4 / 3 ( 3 z 3 ( - 28160 - 1 6 z 2 / 3 - 8640 ( - 1 ) 2 / 3 z 8 / 3 + 162 - 1 6 z 14 / 3 - 81 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 4 + 4320 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 + 14080 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) - 1 ( ( 1 + ) z ) 4 / 3 ( 3 z 3 ( 28160 ( - 1 ) 5 / 6 z 2 / 3 + 8640 - 1 3 z 8 / 3 - 162 ( - 1 ) 5 / 6 z 14 / 3 + 81 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 4 + 4320 2 2 / 3 ( ( 1 + ) z ) 2 / 3 z 2 - 14080 2 2 / 3 ( ( 1 + ) z ) 2 / 3 ) Bi ( - 1 2 3 2 / 3 ( ( 1 + ) z ) 2 / 3 ) ) ) KelvinKer -1 14 3 z -1 -1 3 4 243 2 5 6 3 1 6 z 8 3 1 z 5 3 -1 144 3 1 3 9 z 2 110 2 2 3 1 z 2 3 -1 -1 3 1 2 z 2 3 AiryAi -1 1 2 3 2 3 1 z 2 3 z 1 3 48 3 1 3 110 3 3 1 2 z 2 3 18 -1 1 3 3 1 2 z 8 3 -1 110 2 2 3 3 1 2 1 z 2 3 9 3 1 2 1 z 8 3 2 1 3 -1 AiryBi -1 1 2 3 2 3 1 z 2 3 z 1 3 144 3 1 3 z 9 z 2 110 2 2 3 1 z 1 3 3 1 2 1 z 1 3 AiryAi 1 2 3 2 3 1 z 2 3 1 z 1 3 -1 1 1 z 4 3 -1 3 -14080 2 2 3 1 z 2 3 z 1 3 -1 4320 2 2 3 1 z 2 3 z 7 3 81 2 2 3 1 z 2 3 z 13 3 162 -1 1 6 z 5 -1 8640 -1 2 3 z 3 -1 28160 -1 1 6 z AiryAiPrime 1 2 3 2 3 1 z 2 3 1 1 z 4 3 -1 3 -14080 2 2 3 1 z 2 3 z 1 3 -1 4320 2 2 3 1 z 2 3 z 7 3 81 2 2 3 1 z 2 3 z 13 3 -1 162 -1 1 3 z 5 -1 8640 -1 5 6 z 3 28160 -1 1 3 z AiryAiPrime -1 1 2 3 2 3 1 z 2 3 48 3 1 3 z 9 z 2 110 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 1 z 1 3 -1 -1 1 1 z 4 3 -1 3 1 2 z 1 3 -28160 -1 1 6 z 2 3 -1 8640 -1 2 3 z 8 3 162 -1 1 6 z 14 3 -1 81 2 2 3 1 z 2 3 z 4 4320 2 2 3 1 z 2 3 z 2 14080 2 2 3 1 z 2 3 AiryBiPrime 1 2 3 2 3 1 z 2 3 -1 1 1 z 4 3 -1 3 1 2 z 1 3 28160 -1 5 6 z 2 3 8640 -1 1 3 z 8 3 -1 162 -1 5 6 z 14 3 81 2 2 3 1 z 2 3 z 4 4320 2 2 3 1 z 2 3 z 2 -1 14080 2 2 3 1 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