Tables of Weyl fractional integrals for the Airy function

Functions related to the Weyl fractional integral of the Airy function are tabulated for the 16 lowest orders and for a range of parameters of practical interest. This range, coupled with the asymptotic relations given, covers the entire real axis. The objects of interest are the numerical values and the asymptotic properties of the functions V and W, defined by (1) V(z; n, v; m, ,u) = dt(t z)n I W(t, v) Wm (t, ,u), (2) W(z, n) =fJ0dt(t Z)n Ai(t) (with Ai(x) being the Airy function). They were recently needed to study the properties of atomic nuclei and were not available in the literature. Since they are useful in this context, and might be of mathematical interest, we present them here. In the following we discuss briefly the functions and their asymptotic properties. The numerical tables are given in the microfiche section of this issue. Each function, V and W, is proportional to a Weyl fractional integral [2]. The Weyl fractional integral of an arbitrary function f (t) is defined by