Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes

An absolutely convergent $\alpha$ representation of analytically and (or) dimensionally regularized Feynman.amplitudes is obtained on different sections of the domain of analyticity with respect to the regularizing parameters. The representation differs from the $\alpha$ representation in the original domain of absolute convergence by the presence in the integrand of an operator $\mathscr R^*$, which has the same structure as the $R^*$ operation that generalizes dimensional renormalization when not only ultraviolet but also infrared poles are present. The operator $\mathscr R^*$ explicitly realizes analytic continuation of the parametric integral and can be expressed in terms of the ultraviolet subtracting operators and also in terms of the infrared subtracting operators that generate a Maclaurin expansion in the coordinate space.