On finite analogues of Dobi\'nski's formula and of Euler's constant via Gregory polynomials
Abstract
We study a finite analogue of Dobi\'nski'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 γAW.
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