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We derive the analytical expressions for the first and second order terms inthe hadronic transverse momentum spectra obtained from the Tsallis normalized(Tsallis-1) statistics. We revisit the zeroth order quantum Tsallisdistributions and obtain the corresponding analytical closed form expressions.It is observed that unlike the classical case, the analytical closed forms ofthe zeroth order quantum spectra do not resemble the phenomenologicaldistributions used in the literature after $q \to q^{-1}$ substitution, where$q$ is the Tsallis entropic parameter. However, the factorization approximationincreases the extent of similarity.

Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond