Triple Exponential Smoothing with a high frequency

Hello everyone,

I am trying to develop a forecasting method that is equal to triple exponential smoothing. I cannot use ets() and hw() because my frequency is pretty high with 52 (weekly basis). Therefore I currently use stlf(). However, I am not quite able to figure out how this is mathematically composed in order to interpret it sensibly.

tes <- stlf(train, 
            method = "ets",
            lambda = "auto",
            biasadj = TRUE)

# Output
Forecast method: STL +  ETS(A,Ad,N)

Model Information:

 ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend) 

  Smoothing parameters:
    alpha = 0.0137 
    beta  = 0.0137 
    phi   = 0.9296 

  Initial states:
    l = 2416295.7805 
    b = -1190.9562 

  sigma:  1904907

Is there a possibility to use the triple exponential smoothing according to Holt-Winter's to simply get the three factors (alpha, beta, gamma) and to simplify the comparison to the single and double exponential smoothing?

Thanks a lot for your help.