Convergence and integrability of rational and double rational trigonometric series with coefficients of bounded variation of higher order

We prove that a rational trigonometric series with its coefficients c(n) = o(1) satisfying the condition ?(n?Z) |?(m)c(n)| < 8, m ? N, converges pointwise to some f(x) for every x ? (0, 2p) and also converges in L-p[0, 2 p)-metric to f for 0 < p < (m)/(1). This result is further extended to a double rational trigonometric series.