   Fitting Brack

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Fitting Brack
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
AiGauss( z )  exp   z 2  Brack  z 
The brack term is approximated as
8
Brack  z  
c z
I 1
8
I 1
I
1   cI  8 z I
I 1
The leading constant is 0.4999999999999991 which is off by 9  10-16 from the
theoretical limit. And from the value in the file.
Conclusion
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.
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