  In spite of its undeniable success, there are still open questions regarding
Tsallis non-extensive statistical formalism, whose founding stone was laid in
1988 in JSTAT. Some of them are concerned with the so-called normalization
problem of just how to evaluate expectation values. The Jaynes MaxEnt approach
for deriving statistical mechanics is based on the adoption of (1) a specific
entropic functional form S and (2) physically appropriate constraints. The
literature on non-extensive thermostatistics has considered, in its historical
evolution, four possible choices for the evaluation of expectation values: (i)
1988 Tsallis-original (TO), (ii) Curado-Tsallis (CT), (iii) Tsallis-Mendes-
Plastino (TMP), and (iv) the same as (iii), but using centered operators as
constraints (OLM). The 1988 was promptly abandoned and replaced, mostly with
versions ii) and iii). We will here (a) show that the 1988 is as good as any of
the others, (b) demonstrate that the four cases can be easily derived from just
one (any) of them, i.e., the probability distribution function in each of these
four instances may be evaluated with a unique formula, and (c) numerically
analyze some consequences that emerge from these four choices.
