New series identities with Cauchy, Stirling, and harmonic numbers, and Laguerre polynomials

TL;DR

This paper develops new series identities linking Cauchy numbers, harmonic numbers, Laguerre polynomials, and Stirling numbers using Newton series and binomial formulas, enriching the mathematical understanding of these special sequences.

Contribution

It introduces novel series identities connecting various special numbers and polynomials through innovative use of Newton series and binomial formulas.

Findings

Derived new series identities involving Cauchy, harmonic, and Stirling numbers.

Established connections between Laguerre polynomials and other special sequences.

Enhanced mathematical tools for analyzing special number sequences.

Abstract

In this article we use an interplay between Newton series and binomial formulas in order to generate a number of series identities involving Cauchy numbers, harmonic numbers, Laguerre polynomials, and Stirling numbers of the first kind.