Voronoi means, moving averages, and power series

TL;DR

This paper introduces a novel non-regular generalization of the Nörlund mean, demonstrating its equivalence to a moving average, and establishes theoretical results connecting it with power series and convergence properties.

Contribution

It presents a new non-regular Nörlund mean generalization, linking it to moving averages and deriving related Abelian, Tauberian theorems, and a strong law of large numbers.

Findings

Established equivalence between the generalized Nörlund mean and a moving average.

Proved Abelian and Tauberian theorems relating to convergence and power series.

Proved a strong law of large numbers for the new mean.

Abstract

We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A strong law of large numbers is also proved.