Corpus ID: 20915412

# Asymptotic approximation of central binomial coefficients with rigorous error bounds

@article{Brent2016AsymptoticAO,
title={Asymptotic approximation of central binomial coefficients with rigorous error bounds},
author={Richard P. Brent},
journal={arXiv: Numerical Analysis},
year={2016}
}
• R. Brent
• Published 17 August 2016
• Mathematics, Computer Science
• arXiv: Numerical Analysis
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We also consider some closely related asymptotic series, and make some historical remarks.
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• R. Brent
• Mathematics
• Journal of the Australian Mathematical Society
• 2018
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Probabilistic lower bounds on maximal determinants of binary matrices
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New lower bounds are proved on D(n) and R (n) in terms of d = n-h, where d is the order of a Hadamard matrix and h is maximal subject to $h \le n$. Expand