moving window rms slope

I am trying to calculate the rms slope of a moving window:
zc = elevation of central cell
zb = elevation of cells along the border of the window size
sb = distance of central cell to a border cell
N is the width of window size
To add, I am looking at a 2D matrix
I am having trouble computing the slope.. I have thought of using convolution and diff functions, but they lead to nowhere.
Please advice.
Thanks in advanced!

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