20 citations · 26 across the 9 of their papers we have counts for
11 papers
Sums, series, and products in Diophantine approximation
Jordan Bell
There is not much that can be said for all and for all about the sum \[ \sum_{k=1}^n \frac{1}{|\sin kπx|}. \] However, for this and similar sums, series, and products, we c…
Estimates for the norms of products of sines and cosines
Jordan Bell
In this paper we prove asymptotic formulas for the norms of and . These products can be expressed using $…
Various observations on angles proceeding in geometric progression
Leonhard Euler, Jordan Bell
This is a translation of Euler's 1773 "Variae observationes circa angulos in progressione geometrica progredientes", E561 in the Enestr{ö}m index. I translated this paper as a resu…
On the infinity of infinities of orders of the infinitely large and infinitely small
Leonhard Euler, Jordan Bell
Translation (by J.B.) from the original Latin of Euler's "De infinities infinitis gradibus tam infinite magnorum quam infinite parvorum" (1780). E507 in the Eneström index. Euler d…
Euler and the pentagonal number theorem
Jordan Bell
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partit…
A demonstration of a theorem on the order observed in the sums of divisors
Leonhard Euler, Jordan Bell
Translation from the Latin of Euler's "Demonstratio theorematis circa ordinem in summis divisorum observatum" (1760). E244 in the Enestroem index. In his previous paper E243, Euler…