Re: looking for a suitable numericla method

If I'm not mistaken, the generic expression of the integral,
when b = 1 and 'a' is a positive integer is :

g[a_]=Sqrt[Pi]*(2*Sum[(-1)^(a+k)/E^(a^2-k^2),{k,0,a-1}]+1-(-1)^a/E^a^2)

(in Mathematica notation)

and -g[-a] when 'a' is negative.

v.a.

.