Fundamental formulae and numerical evidences for the central limit theorem in Tsallis statistics

On the way to finding the mathematical structure behind Tsallis statistics, the rigorous formulation of the q-central limit theorem and its proof are expected to play important roles in mathematical physics. This short paper reports some numerical evidences revealing the existence of the central limit theorem in Tsallis statistics reviewing some fundamental formulas such as law of error and q-Stirling's formula.