Finite N\"orlund Summation Methods

TL;DR

This paper discusses simplifications in the theory of Nörlund summation methods when the series of weights converges, providing insights into their properties and applications.

Contribution

It introduces simplified theoretical frameworks for Nörlund summation methods under the condition of convergent weight series.

Findings

Simplified formulas for Nörlund methods when weights sum converges

Enhanced understanding of convergence properties of Nörlund methods

Potential applications in summation theory and series analysis

Abstract

We draw attention to simplifications in the theory of a N\"orlund summation method $(N, p)$ that arise when the series $\sum_{n \geqslant 0} p_n$ is convergent.