Abstract
The code AiGlz.for can be compiled by the command
wfl386 aiglz
This code is designed to give the log of Aigau(z) for values between -30 and -3 using Gauss Laquerre quadrature.
These values appear in ALGAU.OUT.
Gauss Laguerre
Change variables to t’=t-z
0
1
1
2
AiGauss  z  
 exp   t  z  dt ' 

Or
AiGauss  z  

exp   z 2 

For z = 0, AiGauss  0  



0
 exp  t
2
 2tz  z 2 dt

0
 exp  2tz  t dt
2

1

0
 exp  t dt  2
2
1

For z not equal to zero, change variables again to t’=-2tz, so that dt=-dt’/2z
exp   z 2  0

t '2 
AiGauss  z  
exp
t
'

  4 z 2 dt
2 z  
Now let t = - t’
exp   z 2  
 t2 
AiGauss  z  
exp

t
exp
    2 dt
2 z  0
 4z 
This form is appropriate for Gauss Laguerre integration.
Note that the form of interest is

 t2  
Ln( AiGau ( z ))   z 2  ln(2 z )  ln( ) / 2  ln   exp  t  exp   2 dt 
 4z  
0
For small values of z, the integrand becomes a delta function, which is hard to evaluate numerically.
AiGlz.for returns answers to double precision accuracy for z < -3. AIGAUS.OUT contains these values spaced 0.25
apart for z = -103 to z =-3 generated by this code. These codes, a test code and this output are in aiglz.zip