Connection Coefficients for Higher-order Bernoulli and Euler\n Polynomials: A Random Walk Approach

2018/09/12 by Lin Jiu, Jiu, Lin, Christophe Vignat +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1809.04636

openalex publication_date 2018/09/12 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

We consider the use of random walks as an approach to obtain connection\ncoefficients for higher-order Bernoulli and Euler polynomials. In particular,\nwe consider the cases of a 1-dimensional linear reflected Brownian motion and\nof a 3-dimensional Bessel process. Considering the successive hitting times\nof two, three, and four fixed levels by these random walks yields non-trivial\nidentities that involve higher-order Bernoulli and Euler polynomials.\n

Citations

• On a Class of Distributions Stable Under Random Summation

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