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We consider the use of random walks as an approach to obtain connectioncoefficients for higher-order Bernoulli and Euler polynomials. In particular,we consider the cases of a $1$-dimensional linear reflected Brownian motion andof a $3$-dimensional Bessel process. Considering the successive hitting timesof two, three, and four fixed levels by these random walks yields non-trivialidentities that involve higher-order Bernoulli and Euler polynomials.

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