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We prove that a rational trigonometric series with its coefficientsc⁢(n)=o⁢(1){c(n)=o(1)}satisfying the condition∑n∈ℤ|Δm⁢c⁢(n)|&lt;∞{\sum_{n\in\mathbb{Z}}|\Delta^{m}c(n)|&lt;\infty},m∈ℕ{m\in\mathbb{N}}, converges pointwise to somef⁢(x){f(x)}for everyx∈(0,2⁢π){x\in(0,2\pi)}and also converges inLp⁢[0,2⁢π){L^{p}[0,2\pi)}-metric to  f  for0&lt;p&lt;1m{0&lt;p&lt;\frac{1}{m}}. This result is further extended to a double rational trigonometric series.

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