The Airy functions \(\operatorname{Ai}(x)\) and \(\operatorname{Bi}(x)\) are defined by the integral representations,
For further information see Abramowitz & Stegun, Section 10.4.
This routine computes the Airy function \(\operatorname{Ai}(x)\).
This routine computes the Airy function \(\operatorname{Bi}(x)\).
This routine computes a scaled version of the Airy function \(\operatorname{S_A}(x) \operatorname{Ai}(x)\). For \(x > 0\) the scaling factor \(\operatorname{S_A}(x)\) is \(\exp(+(2/3) x^{3/2})\), and is \(1\) for \(x < 0\).
This routine computes a scaled version of the Airy function \(\operatorname{S_B}(x) \operatorname{Bi}(x)\). For \(x > 0\) the scaling factor \(\operatorname{S_B}(x)\) is \(\exp(-(2/3) x^{3/2})\), and is \(1\) for \(x < 0\).
This routine computes the location of the \(s\)-th zero of the Airy function \(\operatorname{Ai}(x)\).
This routine computes the location of the \(s\)-th zero of the Airy function \(\operatorname{Bi}(x)\).
This routine computes the location of the \(s\)-th zero of the Airy function derivative \(\operatorname{Ai}'(x)\).
This routine computes the location of the \(s\)-th zero of the Airy function derivative \(\operatorname{Bi}'(x)\).