The convergence of partial sums of interpolating polynomials

For functions of ΛBV, we study the convergence of the partial sums of interpolating polynomials. An estimate is found for the Fourier–Lagrange coefficients of these functions. For functions in BV, convergence is shown at points of discontinuity if the order of the polynomial increases sufficiently rapidly compared to the order of the partial sum. A Dirichlet–Jordan type theorem is shown for functions of harmonic bounded variation, and this result is shown to be best possible.