A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under either the linear mean energy constraint U or the escort mean energy constraint U_q suffer self-referentiality. In a recent paper Phys. Lett. A 335, 351 (2005)] the authors have shown that the pdfs obtained with either U or U_q are equivalent to the pdf in a non self-referential form. Based on this result we derive an alternative expression for the Tsallis distributions, employing either U or U_q, which is non self-referential.