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arXiv · 1809.04636

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

Lin Jiu·Christophe Vignat
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Abstract

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

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Lin Jiu, Christophe Vignat. 2018-09-12. Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach. https://arxiv.org/abs/1809.04636

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