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Various other relatively simple properties of the functions are also open, including whether it satisfies the traditional exponential functional equation and analogous relations defined for a general exponential by utilizing its inverse, the Artin-Hasse logarithm.

What are a and b here? It is trivial to check that the functional equation isn't satisfied, say, for p=2 and b=2, and this shows that it cannot be satisfied for b being a formal variable either. What is the source for this open question? There seems to be some confusion around. -- Darij (talk) 19:07, 3 January 2013 (UTC)[reply]