PreprintarXiv licencearXiv
On zero distribution of the sum of Gegenbauer polynomials
Abstract
We study the zero distribution of the sum of the first n Gegenbauer polynomials Sn(α)(z)=∑k=0n Ck(α)(z). We prove that for α>1, the zeros of Sn(α)(z) lie on the interval (−1,1) for all large n.
Related
- Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability
- Ratio and limiting zero distribution asymptotics for symmetric multiple orthogonal polynomials
- Romanovski polynomials, Gegenbauer connections, and su(1,1) ladder structures
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- Zero-Density Concentration for Dirichlet Polynomials
BibTeX
@misc{tran2026zero,
title = {{On zero distribution of the sum of Gegenbauer polynomials}},
author = {Khang Tran and Riley White},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38669},
eprint = {2609.38669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38669},
}
RIS
TY - UNPB
TI - On zero distribution of the sum of Gegenbauer polynomials
AU - Khang Tran
AU - Riley White
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38669
UR - https://arxiv.org/abs/2609.38669
AB - We study the zero distribution of the sum of the first n Gegenbauer polynomials S_n^(α)(z)=∑_k=0^n C_k^(α)(z). We prove that for α>1, the zeros of S_n^(α)(z) lie on the interval (−1,1) for all large n.
ER -