need help to clarify ewma() using adjust =TRUE
Hi!

Can someone please help me understand how `adjust = True` in the function `ewma()`  works mathematically?
I understand the idea of simple exponential smoothing and it's basic formula when `adjust = FALSE`,
then alpha is constant, as in the equation:
![daum_equation_1416434433349](https://cloud.githubusercontent.com/assets/8626306/5115295/026b660e-7040-11e4-9c6f-8f41585a2d54.png)
When  `adjusted = True` then I assume that, alpha does not stay constant and it is adjusted "automatically".But what is the **mathematical representaiton** for such case? I've looked into Pandas documentation 
http://pandas.pydata.org/pandas-docs/stable/computation.html#exponentially-weighted-moment-functions 
and there it says that when it is **adjusted**, then the function uses this weights:
![daum_equation_1416434874359](https://cloud.githubusercontent.com/assets/8626306/5115494/e84f2e66-7041-11e4-80c0-dc863387c09f.png)

It is still not clear to me how this adjustment is working. 

The only simple exponential method using an adaptive/adjusting alpha that I know of, is from Rob Hyndman's book: "Forecasting Methods and Application" .There I found a variation of the simple exponential smoothing (p.155-157), where alpha is adjusted automatically, called "adaptive-respose single exponential smoothing" (ARRSES). Unfortunately I got different results from each, so I guess this is not the one.

Does anybody know how to explain this specific case mathematically? or knows a good reference?

Thanks!
