arXiv subjects

Christopher N. B. Hammond

Publications and source records attributed to Christopher N. B. Hammond.

4 recordsLinked to original sources

arXiv2019

The Case for Raabe's Test

Among the techniques for determining the convergence of a series, Raabe's Test remains relatively unfamiliar to most mathematicians. We present several results relating to Raabe's Test that do not seem to be widely known, making the case that Raabe's Test should be featured more prominently in undergraduate calculus and analysis courses. In particular, we demonstrate that Raabe's Test may be viewed as an implicit comparison with a $p$-series, in the same manner that the Ratio Test and the Root Test constitute an implicit comparison with a geometric series. Moreover, Raabe's Test can sometimes simplify the process for determining conditional convergence.

math.HO↗

arXiv2018

Regular Variation and Raabe

There are many tests for determining the convergence or divergence of series. The test of Raabe and the test of Betrand are relatively unknown and do not appear in most classical courses of analysis. Also, the link between these tests and regular variation is seldomly made. In this paper we offer a unified approach to some of the classical tests from a point of view of regular varying sequences.

math.CA↗

arXiv2015

Multi-Opponent James Functions

The James function, also known as the "log5 method," assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, explores the analogous situation where a single team or player competes simultaneously against multiple opponents.

math.ST↗

arXiv2014

The James Function

We investigate the properties of the James function, associated with Bill James's so-called "log5 method," which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also introduce and study a class of functions, which we call Jamesian, that satisfy the same a priori conditions that were originally used to describe the James function.

math.HO↗