On some sequences of polynomials generating the Genocchi numbers

TL;DR

This paper explores polynomial sequences that generate Genocchi numbers, developing a new representation approach and deriving generalized identities to deepen understanding of these special number sequences.

Contribution

Introduces a polynomial-based representation of Genocchi numbers and constructs generalized identities extending known results.

Findings

New polynomial sequences generating Genocchi numbers

Generalized identities for Genocchi numbers

Enhanced understanding of number sequence representations

Abstract

Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities generalizing the known identities are constructed.