Asymptotic analysis of nested derivatives

TL;DR

This paper provides an asymptotic analysis of nested derivatives of functions as the order increases, employing a discrete ray method and validating results with examples.

Contribution

It introduces a novel asymptotic approach to analyze nested derivatives using a discrete ray method, with practical accuracy demonstrations.

Findings

Asymptotic formulas accurately approximate nested derivatives for large n.

The discrete ray method effectively analyzes the growth of nested derivatives.

Examples confirm the validity of the asymptotic analysis.

Abstract

We analyze the nested derivatives of a function $\mathfrak{D}^{n}[f]\,(x)$ asymptotically, as $n\rightarrow\infty,$ using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.