Recurrences and Congruences for Higher order Geometric Polynomials and Related Numbers

TL;DR

This paper develops new recurrence relations, explicit formulas, and convolution identities for higher order geometric polynomials, extending known results and establishing congruences for related numbers like p-Bernoulli numbers.

Contribution

It introduces generalized recurrence relations and identities for higher order geometric polynomials, expanding the theoretical framework and connecting to p-Bernoulli numbers.

Findings

New recurrence relations for higher order geometric polynomials

Explicit formulas and convolution identities derived

Congruences established for p-Bernoulli numbers

Abstract

We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order geometric polynomials, particularly for p-Bernoulli numbers.