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Moment representations for generalized Lehmer polynomials
Abstract
We represent normalized generalized Lehmer polynomials as moments of a random variable constructed from two independent negative binomial variables and an independent uniform variable. An integral form of their known exponential generating function yields mixtures of uniform distributions and convergent double series. We recover Eulerian polynomial identities and give a probabilistic interpretation of anti-diagonal sums of poly-Bernoulli numbers. We also prove moment determinacy, characterize the Stieltjes parameter range, derive Hankel total non-negativity and log-convexity, and identify the boundary distributions.
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BibTeX
@misc{ikeda2026moment,
title = {{Moment representations for generalized Lehmer polynomials}},
author = {Karin Ikeda and Hideki Murahara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36409},
eprint = {2610.36409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36409},
}
RIS
TY - UNPB
TI - Moment representations for generalized Lehmer polynomials
AU - Karin Ikeda
AU - Hideki Murahara
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36409
UR - https://arxiv.org/abs/2610.36409
AB - We represent normalized generalized Lehmer polynomials as moments of a random variable constructed from two independent negative binomial variables and an independent uniform variable. An integral form of their known exponential generating function yields mixtures of uniform distributions and convergent double series. We recover Eulerian polynomial identities and give a probabilistic interpretation of anti-diagonal sums of poly-Bernoulli numbers. We also prove moment determinacy, characterize the Stieltjes parameter range, derive Hankel total non-negativity and log-convexity, and identify the boundary distributions.
ER -