On finite analogues of Dobiński's formula and of Euler's constant via Gregory polynomials

Abstract

We study a finite analogue of Dobiński's formula, which is related to the Napier constant $e$, and its Bessel-type generalizations. Furthermore, using Gregory polynomials, we extend the results of Kaneko--Matsusaka--Seki on finite analogues of Euler's constant, and compare them with the Wilson-type analogue ${\gamma }_{\mathcal{A}}^{\mathrm{W}}$.

14 pages