Gauss Legendre
AiGauss  f   AiGauss  f 0  
1

f
 exp  t  dt
2
f0
The integral is evaluated using 6 and 7 Gauss Legendre quadrature points and weights. The error is estimated as the
difference between 6 point quadrature and 7 point quadrature. The first value at f0 is found using the method described
in Gauss Laguerre.doc. There is a minor problem of adding numbers too large or small to be represented as reals that is
treated in gleg\Relad.doc.
TGLEG67.FOR  GLEG.zip
Modification
Let t’=t-f
AiGauss  f   AiGauss  f 0  
1

0


2

2

exp   t ' f  dt '
f0  f
Let t = -t’
AiGauss  f   AiGauss  f 0  
1

0


exp   t  f  dt
f  f0
Reverse the integration order to find
f  f0
1
2
AiGauss  f   AiGauss  f 0  
 exp  t  f  dt

AiGauss  f   AiGauss  f 0  


0
exp   f 2 
f  f0

exp  2 ft  t 2  dt

0
This should make no difference aigau15m.for