GNU Scientific Library – Reference Manual: Airy Functions and Derivatives

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### 7.4 Airy Functions and Derivatives

The Airy functions Ai(x) and Bi(x) are defined by the integral representations,

    Ai(x) = (1/\pi) \int_0^\infty \cos((1/3) t^3 + xt) dt
    Bi(x) = (1/\pi) \int_0^\infty (e^(-(1/3) t^3 + xt) + \sin((1/3) t^3 + xt)) dt

For further information see Abramowitz & Stegun, Section 10.4. The Airy functions are defined in the header file `gsl_sf_airy.h`.