A note on some applications of the extension of Abel's lemma

TL;DR

This paper explores new applications of an extended form of Abel's lemma, highlighting its connection to series involving the Riemann zeta function, and broadening its mathematical utility.

Contribution

It introduces novel applications of an extended Abel's lemma and links it to Riemann zeta series, expanding its theoretical significance.

Findings

New applications of Abel's lemma are demonstrated.

A connection between Abel's lemma and Riemann zeta series is established.

The work broadens the understanding of Abel's lemma's utility.

Abstract

We offer some new applications of an extension of Abel's lemma, as well as its more general form established by Andrews and Freitas. A nice connection is established between this lemma and series involving the Riemann zeta function.