I have a series of the form
F(x) = A_1 exp(-a_1*x) + A_2 exp(-a_2*x) + ... + A_N exp(-a_N*x)
Is there a formula for the quantity F(x)^m that is simple to evaluate?
I can do m nested loops and obtain the coefficients and exponents for F(x)^m, but this is very resource consuming if N and m are large. Typical values of N is in the 10s or 100s, m can be as high as 25.
I am looking for something similar to the bionomial sum.
Thank you in advance.