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arXiv · 2508.17189

Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials

Taekyun Kim·Dae San Kim
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Abstract

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and probabilistic degenerate Frobenius-Euler polynomials associated with Y , and more generally of their higher-order counterparts. We derive explicit formulas with the help of umbral calculus and illustrate our results in the case of several random variables Y

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Taekyun Kim, Dae San Kim. 2025-08-24. Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials. https://arxiv.org/abs/2508.17189

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