Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach
Number Theory
2018-09-14 v1 Probability
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 -dimensional linear reflected Brownian motion and of a -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.
Keywords
Cite
@article{arxiv.1809.04636,
title = {Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach},
author = {Lin Jiu and Christophe Vignat},
journal= {arXiv preprint arXiv:1809.04636},
year = {2018}
}