Derivative of the Airy function Ai: Integration (formula 03.07.21.0016)

AiryAiPrime

$Mathematica Notation$

Bessel-Type Functions

AiryAiPrime[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving exponential function and a power function

Involving exp and power

Linear arguments

http://functions.wolfram.com/03.07.21.0016.01

Input Form

Integrate[Sqrt[z] E^((2/3) (a z)^(3/2)) AiryAiPrime[a z], z] == (1/(21 a^2 Sqrt[z] Gamma[1/3])) (6 a^2 E^((2/3) (a z)^(3/2)) z^2 AiryAiPrime[a z] Gamma[1/3] + 2 Sqrt[a z] (2 3^(2/3) + (a^3 E^((2/3) (a z)^(3/2)) z^3 BesselI[-(5/3), (2/3) a^(3/2) z^(3/2)] Gamma[1/3])/(a^(3/2) z^(3/2))^(1/3) - a^2 E^((2/3) (a z)^(3/2)) z^2 (a^(3/2) z^(3/2))^(1/3) BesselI[5/3, (2/3) a^(3/2) z^(3/2)] Gamma[1/3]))

Standard Form

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MathML Form

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Rule Form

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

2001-10-29