On Apostol-Type Mersenne-Bernoulli and Mersenne-Euler Polynomials

Artatrana Suna; Prasanta Kumar Ray

doi:10.1051/ita/2026017

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arXiv · 2606.28400

On Apostol-Type Mersenne-Bernoulli and Mersenne-Euler Polynomials

Artatrana Suna·Prasanta Kumar Ray

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Abstract

In this paper, we introduce the Apostol-type Mersenne-Bernoulli and Mersenne-Euler polynomials of order $\alpha$. By employing the $M$-calculus, based on the Mersenne numbers, we establish explicit series representations, addition theorems, difference equations and convolution identities.

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Artatrana Suna, Prasanta Kumar Ray. 2026-06-24. On Apostol-Type Mersenne-Bernoulli and Mersenne-Euler Polynomials. https://doi.org/10.1051/ita%2F2026017

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