Well, 1st in your expression there are square-brackets around Epsilon. That may give difficulties beacuse of the special use of square-brackets in Mathematica. If you delete them you get
In[2]:= Hypergeometric1F1[
1.99997 - (0.00729735 Epsilon)/Sqrt[1 - Epsilon^2], 2.99995,
274.449 Sqrt[1 - Epsilon^2]]
Out[2]= Hypergeometric1F1[
1.99997 - (0.00729735 Epsilon)/Sqrt[1 - Epsilon^2], 2.99995,
274.449 Sqrt[1 - Epsilon^2]]
So as remarked by Sean Epsilon is not defined. If you do that you get a (quite big) number
In[4]:= Epsilon = .01;
Hypergeometric1F1[ 1.99997 - (0.00729735 Epsilon)/Sqrt[1 - Epsilon^2], 2.99995,
274.449 Sqrt[1 - Epsilon^2]]
Out[4]= 1.11327*10^117
Regards, Hans