very large valued function

Hello, I want to represent the Dawson function

with its Maclaurin expansion of 41 terms in the form

I want this expression be used in a nonlinear programming problem (to be solved with function fmincon) and after in a plot (b,t) when a and eta are computed. Because large (infinite) numbers appear, matlab cannot deal with this. I tried several ways to avoid this, such as using taylor series for the exponential, so as to use for loops and avoiding infinite numbers by performing subtractions, but no correct results occur.

How can I deal with this?

Answer 1

[Konstantinos]

the paper says that fmincon gives a=0.31, eta=5437.9. So, if we take this numbers, how can b(t,a,eta) be plotted? Matlab has dawson function for the case

and not for this case here. So it has to be approximated by the series.