Some identities which involve Stirling numbers

TL;DR

This paper presents new mathematical identities involving Stirling numbers and binomial coefficients, discovered during research on parton distribution functions at small-x, contributing to combinatorial mathematics.

Contribution

It introduces several identities linking Stirling numbers and binomial coefficients, expanding the mathematical toolkit relevant to combinatorics and theoretical physics.

Findings

Identities involving Stirling numbers of the first and second kind.

Connections between Stirling numbers and binomial coefficients.

Potential applications in analyzing parton distribution functions.

Abstract

During the course of an ongoing work on the small-$x$ behaviour of parton distribution functions, some identities have been found which involve Stirling numbers of the first and the second kind, as well as binomial coefficients. Without any claim of originality I report them in this note.