# How to build a function with the result of arima in R?

I use: arima(y, order = c(3,1,1) in R to get ARIMA(3,1,1), result as follows:

Call: arima(x = y, order = c(3,1,1))

Coefficients:

       ar1     ar2      ar3      ma1
0.2275  0.0823  -0.0986  -0.9500
s.e. 0.0633  0.0632   0.0624   0.0222


sigma^2 estimated as 4.802e+09:
log likelihood = -3745.37,
aic = 7500.73

How can I make a formula with this result, I thought of something like this

Y(t+1) = (1+0,2275)*Yt + (0,2275-0,0823)*Yt-1 + (0,0823+0,0986)*Yt-2 + 0,0986*Yt-3 + et+1 + θ_1*ε_T

But i don't know if this is right, and what the error is at point T