Abstract: Bose gases hold significant research importance in statistical physics and quantum thermodynamics, as their energy distribution characteristics directly determine the thermodynamic behavior of systems. This paper focuses on ideal Bose systems in equilibrium states and derives a universal expression for variousorder energy moments (i.e., power averages of energy) based on the features of BoseEinstein integrals. This expression achieves a unified characterization of energy statistical properties in Bose systems without relying on system dimensionality or distinguishing between relativistic and nonrelativistic frameworks. The obtained results provide a simple and effective analytical method for the indepth study of physical quantities such as the average number of excited particles, the average energy, and the energy fluctuations in bosonic systems. Additionally, through specific model validations, this paper confirms the correctness and applicability of the expression, demonstrating its broad applicability and potential for generalization in quantum statistical computations and thermodynamic analyses.

Key words: quantum statistics, Boson, energy moments, BoseEinstein integral