Figure 1 Fxy-FA
The fit is a Pade to data generated by gendat which is included in FittingBrack.zip. The fit is to the bracket in
The brack term is approximated as
The leading constant is 0.4999999999999991 which is off by 9 ´ 10-16 from the theoretical limit. And from the value in the file.
The fit is clearly more accurate than the data generated by gendat. In particular, the approximation of AiGauss(x) changes from the Laguerre integral to Gauss-Legendre at z = -3 which is approximately where the fit breaks down.
Figure 2 Detail of the "glitch"
The value calculated
is at -2.625. It is only slightly in
error, the integration from this to -2.8375 contributes the bulk of the
error. This is a seven point
Gauss-Legendre Quadrature. An easy
correction is to halve the first interval.