  We expand the Tsallis distribution in a Taylor series of powers of (q-1),
where q is the Tsallis parameter, assuming q is very close to 1. This helps in
studying the degree of deviation of transverse momentum spectra and other
thermodynamic quantities from a thermalized Boltzmann distribution. After
checking thermodynamic consistency, we provide analytical results for the
Tsallis distribution in the presence of collective flow up to the first order
of (q-1). The formulae are compared with the experimental data.
