On Mersenne-Bernoulli and Mersenne-Euler polynomials

Artatrana Suna; Prasanta Kumar Ray

On Mersenne-Bernoulli and Mersenne-Euler polynomials

综合数学 2026-06-30 v1

作者: Artatrana Suna , Prasanta Kumar Ray

摘要

The sequence of Mersenne numbers $\{M_n\}_{n\geq 0}$ is defined as $M_n = 2^n-1.$ In this study we introduce the Mersenne-Bernoulli and Mersenne-Euler polynomials. Using the generating functions and $M$ -calculus we find some identities associated with them. Moreover, we define the corresponding matrices with these polynomials, factorise them and find their inverses.

引用

@article{arxiv.2607.01269,
  title  = {On Mersenne-Bernoulli and Mersenne-Euler polynomials},
  author = {Artatrana Suna and Prasanta Kumar Ray},
  journal= {arXiv preprint arXiv:2607.01269},
  year   = {2026}
}