On the cut-off prescriptions associated with power-law generalized thermostatistics

We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter q>1 we advance an alternative cut-off prescription and discuss some of its basic mathematical properties. As an illustration of the new cut-off prescription we consider in some detail the q-generalized quantum distributions which have recently been shown to reproduce various experimental results related to high Tc superconductors.