8 citations · 10 across the 13 of their papers we have counts for
8 papers · 1 filter
On a problem on partitions into distinct primes
John M. Campbell
For a positive integer , we write in place of the maximum number of distinct primes whose sum is , assuming there is a way of writing as a sum of distinct primes,…
On a conjecture on a series of convergence rate
John M. Campbell
Sun, in 2022, introduced a conjectured evaluation for a series of convergence rate involving harmonic numbers. We prove both this conjecture and a stronger version of…
Hyperbolic summations derived using the Jacobi functions and
John M. Campbell
We introduce a method that is based on Fourier series expansions related to Jacobi elliptic functions and that we apply to determine new identities for evaluating hyperbolic infini…
On a problem involving the squares of odd harmonic numbers
John M. Campbell, Paul Levrie, Ce Xu +1
We introduce a full solution to a problem considered by Wang and Chu concerning series involving the squares of finite sums of the form .…
On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
John M. Campbell, Jacopo D'Aurizio, Jonathan Sondow
Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integra…
Ramanujan-Type Series Related to Clausen's Product
John M. Campbell
Infinite series are evaluated through the manipulation of a series for resulting from Clausen's Product. Hypergeometric series equal to an expression involvin…