Providing an analytical solution for internal energy of harmonic oscillator from Tsallis statistical mechanics perspective

Many studies have been reported on the nonextensive thermodynamics since Tsallis proposedthe so-call Tsallis entropy [1]. The Tsallis nonextensive statistics has been successfullyapplied to a wide range of nonextensive systems including physics, chemistry, astronomy,geophysics, biology, economics, and others[3].In this article, we will work out the vibrationpartition function within the Tsallis non-extensive statistical mechanics with infinite levelswhen 1