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; }

 AiryAiPrime

 http://functions.wolfram.com/03.07.21.0024.01

 Input Form

 Integrate[Cosh[b + (2/3) (a z)^(3/2)] AiryAiPrime[a z], z] == (E^(-b - (2/3) (a z)^(3/2)) (-2 3^(1/3) E^((2/3) (a z)^(3/2)) (a^(3/2) z^(3/2))^(2/3) - 2 3^(1/3) E^((2/3) (3 b + (a z)^(3/2))) (a^(3/2) z^(3/2))^(2/3) - 6 (-1 + E^(2 b + (4/3) (a z)^(3/2))) (a z)^(3/2) (a^(3/2) z^(3/2))^(2/3) AiryAi[a z] Gamma[5/3] + 15 a (1 + E^(2 b + (4/3) (a z)^(3/2))) z (a^(3/2) z^(3/2))^(2/3) AiryAiPrime[a z] Gamma[5/3] - 3 a^3 z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[5/3] - 3 a^3 E^(2 b + (4/3) (a z)^(3/2)) z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[5/3] + (3 a^4 z^4 BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[5/3])/ (a^(3/2) z^(3/2))^(2/3) + (1/(a^(3/2) z^(3/2))^(2/3)) (3 a^4 E^(2 b + (4/3) (a z)^(3/2)) z^4 BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[5/3])))/(30 a (a^(3/2) z^(3/2))^(2/3) Gamma[5/3])

 Standard Form

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 MathML Form

 cosh ( 2 3 ( a z ) 3 / 2 + b ) Ai ( a z ) z 1 30 a ( a 3 / 2 z 3 / 2 ) 2 / 3 Γ ( 5 3 ) ( - 1 3 2 ( a z ) 3 / 2 - b ( - 6 ( - 1 + 4 3 ( a z ) 3 / 2 + 2 b ) ( a 3 / 2 z 3 / 2 ) 2 / 3 Ai ( a z ) Γ ( 5 3 ) ( a z ) 3 / 2 - 2 3 3 2 3 ( a z ) 3 / 2 ( a 3 / 2 z 3 / 2 ) 2 / 3 - 2 3 3 2 3 ( ( a z ) 3 / 2 + 3 b ) ( a 3 / 2 z 3 / 2 ) 2 / 3 + 15 a ( 1 + 4 3 ( a z ) 3 / 2 + 2 b ) z ( a 3 / 2 z 3 / 2 ) 2 / 3 Ai ( a z ) Γ ( 5 3 ) + 3 a 4 Γ ( 5 3 ) ( a 3 / 2 z 3 / 2 ) 2 / 3 4 3 ( a z ) 3 / 2 + 2 b z 4 I 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) + 3 a 4 z 4 Γ ( 5 3 ) ( a 3 / 2 z 3 / 2 ) 2 / 3 I 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) - 3 a 3 4 3 ( a z ) 3 / 2 + 2 b z 3 I - 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 5 3 ) - 3 a 3 z 3 I - 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 5 3 ) ) ) z 2 3 a z 3 2 b AiryAiPrime a z 1 30 a a 3 2 z 3 2 2 3 Gamma 5 3 -1 -1 1 3 2 a z 3 2 -1 b -6 -1 4 3 a z 3 2 2 b a 3 2 z 3 2 2 3 AiryAi a z Gamma 5 3 a z 3 2 -1 2 3 1 3 2 3 a z 3 2 a 3 2 z 3 2 2 3 -1 2 3 1 3 2 3 a z 3 2 3 b a 3 2 z 3 2 2 3 15 a 1 4 3 a z 3 2 2 b z a 3 2 z 3 2 2 3 AiryAiPrime a z Gamma 5 3 3 a 4 Gamma 5 3 a 3 2 z 3 2 2 3 -1 4 3 a z 3 2 2 b z 4 BesselI 4 3 2 3 a 3 2 z 3 2 3 a 4 z 4 Gamma 5 3 a 3 2 z 3 2 2 3 -1 BesselI 4 3 2 3 a 3 2 z 3 2 -1 3 a 3 4 3 a z 3 2 2 b z 3 BesselI -1 4 3 2 3 a 3 2 z 3 2 Gamma 5 3 -1 3 a 3 z 3 BesselI -1 4 3 2 3 a 3 2 z 3 2 Gamma 5 3 [/itex]

 Rule Form

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

 2001-10-29