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arXiv · 2510.21558

Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials

Dae san Kim·Taekyun Kim
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Abstract

We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable $Y$, whose moment generating function exists in a neighborhood of the origin. In addition, this paper explores the problem of representing arbitrary polynomials in terms of their higher-order counterparts. We develop explicit formulas for those representations with the help of umbral calculus and illustrate our results for several discrete and continuous random variables Y.

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Dae san Kim, Taekyun Kim. 2025-10-24. Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials. https://arxiv.org/abs/2510.21558

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