Qu, C. K.; Wong, R. Szegö’s conjecture on Lebesgue constants for Legendre series. (English) Zbl 0664.42012 Pac. J. Math. 135, No. 1, 157-188 (1988). In 1926, Szegö conjectured that the Lebesgue constants for Legendre series form a monotonically increasing sequence. In this paper, we prove that his conjecture is true. Our method is based on an asymptotic expansion together with an explicit error bound, and makes use of some recent results of Baratella and Gatteschi concerning uniform asymptotic approximations of the Jacobi polynomials. Cited in 1 ReviewCited in 15 Documents MSC: 42C15 General harmonic expansions, frames Keywords:Lebesgue constants for Legendre series; error bound; uniform asymptotic approximations of the Jacobi polynomials PDFBibTeX XMLCite \textit{C. K. Qu} and \textit{R. Wong}, Pac. J. Math. 135, No. 1, 157--188 (1988; Zbl 0664.42012) Full Text: DOI