Abstract: The α₃ coefficient of scalar field in arbitrary Riemann space-time background is calculated by point separation method in this article. The primary expression of α₃ involves 25 invariants. Using the identities derived in the appendix, we can reduce α₃ from 25 invariants to 17 invariants which agree with Gilkey's formula for α₃ coefficient of the scalar field derived by geometric methods and reasons. Recently we derived two important invariant identilies, using these identities we can reduce α₃ from 17 invariants to 15 invariants which would much simplify the calculation of the energymomentum tensor of vacuum polarization.