@article{3e0df53c594747629e3732754548ad74,

title = "Maximizing weighted sums of binomial coefficients using generalized continued fractions",

abstract = "Let and satisfy and. Our main result is a generalized continued fraction for an expression involving the partial binomial sum. We apply this to create new upper and lower bounds for and thus for. We also bound an integer such that. For real g{\omega,m}(m)$> and \cdots > we prove that, and also for or and.",

keywords = "binomial coefficients, bounds, continued fraction, partial sum",

author = "Glasby, {S. P.} and Paseman, {G. R.}",

note = "Publisher Copyright: Copyright {\textcopyright} The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.",

year = "2024",

month = aug,

day = "27",

doi = "10.1017/prm.2024.46",

language = "English",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

publisher = "Cambridge University Press",

}