Some Identities Related to the Second-Order Eulerian Numbers
Amy M. Fu
TL;DR
This paper explores relationships between Nörlund polynomials, second-order Eulerian numbers, and Bernoulli numbers, providing new identities and a concise proof for a previously posed problem.
Contribution
It introduces novel identities linking these mathematical objects and offers a simplified proof for an existing open problem.
Findings
Expressed Nörlund polynomials via second-order Eulerian numbers
Derived new identities involving Bernoulli numbers
Provided a short proof for Rzadkowski and Urliadkska's problem
Abstract
We express the N\"{o}rlund polynomials in terms of the second-order Eulerian numbers. Based on this expression, we derive several identities related to the Bernoulli numbers. In particular, we present a short proof of the problem raised by Rz\c{a}dkowski and Urli\'{n}ska.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Functional Equations Stability Results