Factorials and powers, a minimality result, revisited
David E. Radford
TL;DR
This paper revisits the minimality of the smallest positive integer n such that a^n < n! for a given a > 1, exploring related sequences and their properties in mathematical analysis.
Contribution
It extends previous studies by further examining the properties of sequences related to the minimal n satisfying a^n < n! for real a > 1.
Findings
Analysis of the behavior of the minimal n for different values of a
Identification of new properties of the associated sequences
Comparison with prior results in factorial and power inequalities
Abstract
Let . Then for some positive integer . There are several numerical sequences associated with the study of the smallest such integer which are studied in \cite{RadFact} and \cite{RadGamma}. Here we continue the examination of one of them.
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Taxonomy
TopicsCoding theory and cryptography · Mathematical Approximation and Integration · graph theory and CDMA systems