Zeros of Sections of the Binomial Expansion

TL;DR

This paper investigates the asymptotic distribution of zeros of partial sums of the binomial expansion, providing insights into their behavior as parameters grow large.

Contribution

It offers a new analysis of the zero distribution of binomial expansion sections, extending understanding of their asymptotic properties.

Findings

Zeros exhibit specific asymptotic patterns

Distribution converges to a particular curve or set

Results enhance understanding of polynomial zero behavior

Abstract

We examine the asymptotic behaviour of the zeros of sections of the binomial expansion. That is, we consider the distribution of zeros of $\displaystyle B_{r,n}(z) = \sum_{k=0}^r {n \choose k} z^k$, where $1 \le r < n$.