Sharp bounds for some segments of bounded power series

2025/07/06 by Kovalev, Leonid V.
#30H10 #30J10 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30B10 #Secondary 30C15

paper · doi:10.48550/arxiv.2507.04544

Abstract

We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in the unit disk.

Citations

• Zeros of Sections of the Binomial Expansion
• Differentiably Finite Power Series

Related

• Bounded Power Series on the Real Line
• Sharp Taylor Polynomial Enclosures in One Dimension
• On the class of dominant and subordinate products
• The Lagrangian remainder of Taylor's series, distinguishes O(f(x)) time complexities to polynomials or not
• Inequalities for the exponential remainder of the Taylor series