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On questions posed by Gundersen and Yang concerning a certain binomial differential equation
Abstract
Suppose a, b, c are polynomials with ab ≠ 0 and c nonconstant. We determine all entire solutions to the equation f'f'' − a(z)f2 = b(z)e2c(z). This completely solves two open questions posed by Gundersen and Yang in [Comput. Methods Funct. Theory 21 (2021), 605-617].
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BibTeX
@misc{xiang2026questions,
title = {{On questions posed by Gundersen and Yang concerning a certain binomial differential equation}},
author = {Xuxu Xiang and Jianren Long},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15582},
eprint = {2609.15582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15582},
}
RIS
TY - UNPB
TI - On questions posed by Gundersen and Yang concerning a certain binomial differential equation
AU - Xuxu Xiang
AU - Jianren Long
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15582
UR - https://arxiv.org/abs/2609.15582
AB - Suppose a, b, c are polynomials with ab ≠ 0 and c nonconstant. We determine all entire solutions to the equation f'f'' − a(z)f^2 = b(z)e^2c(z). This completely solves two open questions posed by Gundersen and Yang in [Comput. Methods Funct. Theory 21 (2021), 605-617].
ER -