Consider a sequence $x=(x_1,x_2,x_3)$ and the "padded" version $\hat x = (x_1,x_2,x_3,0,0,\ldots)$ with zeros all the way to infinity.
What is the standard way to refer to $\hat x$ with respect to $x$? I have searched for "padded sequence" and "infinite extension of a sequence" but haven't found much. Perhaps making a connection to mappings (every sequence is a mapping) will reveal the correct terminology? Any relevant terms would be appreciated.