Regular expansion for calculation of the renormalization-group functions in a theory with dimensional coupling constants

A new regular (possessing a small parameter $\zeta$) expansion for calculating the renormalization-group functions in the theory with interaction $g\Phi^4+\lambda\Phi^6$ directly in three-dimensional space is constructed. Depending on the values of the renormalized charges, the theory exhibits regular tricritical or critical behavior. The critical exponents calculated in the first order in $\zeta$ are equal to those calculated in the framework of the $4-\varepsilon$-expansion.