Newman-Rivlin asymptotics for partial sums of power series

2015/03/14 by Antonio R. Vargas, Vargas, Antonio R.
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CV

paper · pdf · doi:10.48550/arxiv.1503.04262

18 pages, 2 figures

arxiv created 2015/03/14 · openalex publication_date 2015/03/14 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss analogues of Newman and Rivlin's formula concerning the ratio of a partial sum of a power series to its limit function and present a new general result of this type for entire functions with a certain asymptotic character. The main tool used in the proof is a Riemann-Hilbert formulation for the partial sums introduced by Kriecherbauer et al. This new result makes some progress on verifying a part of the Saff-Varga Width Conjecture concerning the zero-free regions of these partial sums.

Citations

• The zeros of the partial sums of the exponential function∗

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