6 papers
The finitude of the fibers of the complementary Bell numbers
John M. Campbell
Subbarao and Verma introduced, in 1999, a number of open problems concerning the sequence of complementary Bell numbers, which may be defined via Bell polynomia…
On the binary digits of the Erdős-Borwein constant
John M. Campbell
In a landmark paper on arithmetical properties of Lambert series, Erdős proved that is irrational. This value is now referred to as th…
On divisor sums due to Erdős and Ramanujan
John M. Campbell
Let denote the number of divisors of a positive integer . A classical problem in analytic number theory is given by the asymptotic behavior of the divisor sum $\sum_{n \l…
-analogues of -formulas due to Ramanujan and Guillera
John M. Campbell
The first known -analogues for any of the formulas for due to Ramanujan were introduced in 2018 by Guo and Liu (J. Difference Equ. Appl. 29:505-513, 2018), via…
On the minimal polynomials of the arguments of dilogarithm ladders
John M. Campbell
Letting denote a polylogarithm ladder of weight and index with as an algebraic number, there is a rich history surrounding how mathematical objects of thi…
A further -analogue of a formula due to Guillera
John M. Campbell
Hou, Krattenthaler, and Sun have introduced two -analogues of a remarkable series for due to Guillera, and these -identities were, respectively, proved with the use of…