Taslakyan, A. K. Estimate of the coefficients of a generalized Fourier-Legendre series. (Russian) Zbl 0779.42015 Matematika 6, 60-66 (1988). Let \(f\) be a function of bounded variation on [0,1], \(F(x):=\int^ x_ 0f(t)dt\), and \(a_ n\) the \(n\)th Fourier coefficient of \(F\) with respect to the Legendre quasipolynomials \(\{P_ n(x):n\geq 0\}\). The author proves an estimate on \(a_ n\), whence he deduces the absolute and uniform convergence of the expansion of \(F\) with respect to \(\{P_ n\}\) on every interval inside (0,1). Reviewer: F.Móricz (Szeged) MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Keywords:Fourier-Legendre series; Fourier coefficient; Legendre quasipolynomials; absolute and uniform convergence; expansion PDFBibTeX XMLCite \textit{A. K. Taslakyan}, Matematika 6, 60--66 (1988; Zbl 0779.42015)