Radial flow in non-extensive thermodynamics and study of particle spectra at LHC in the limit of small (q - 1)

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. (orig.)