1 citations · 1 across the 4 of their papers we have counts for
5 papers
On a Notion of Density Related to Restricted Diophantine Approximation
Chance Sanford
We introduce notion of density for a subset of the natural numbers called the Diophantine density. First, we demonstrate that the Diophantine density is an abstract density in the…
A Note on Diophantine Approximation with Restricted Denominators
Chance Sanford
In this note we explore rational approximations to irrational numbers whose denominators are restricted to a subset of the natural numbers. We introduce a specific notion of densit…
A Dilogarithm Series and a Generalization of a Theorem of Bridgeman
Chance Sanford
Using Abel's five-term relation, we derive a new two-parameter series identity for the Rogers dilogarithm. By specializing this identity, we obtain dilogarithm series involving Luc…
Two Neumann Series Expansions for the Sine and Cosine Integrals
Chance Sanford
In this work, series expansions in terms of Bessel functions of the first kind are given for the sine and cosine integrals. These representations differ from many of the known Neum…
Infinite Series Involving Fibonacci Numbers Via Apéry-Like Formulae
Chance Sanford
In this note, infinite series involving Fibonacci and Lucas numbers are derived by employing formulae similar to that which Roger Apéry utilized in his seminal paper proving the ir…