Convergence rates for exponential interpolation series

An analysis of the rate of convergence is made for the interpolation series based on the biorthogonal system (_n^Δ)ƒ(0) and e_n(z) = Δⁿx^z ¦_x−1, which was recently shown to be convergent for certain entire functions of exponential type. An error bound is obtained which is shown to vary as a negative power of the number of terms in the partial sum. Comparison is made with numerical calculations in a few simple cases and certain practical applications are mentioned.