8 citations · 10 across the 13 of their papers we have counts for
14 papers
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,…
A Combinatorial Hopf Algebra on Partition Diagrams
John M. Campbell
We introduce a Combinatorial Hopf Algebra (CHA) with bases indexed by the partition diagrams indexing the bases for partition algebras. By analogy with the operation $H_α H_β = H_{…
On two-term hypergeometric recursions with free lower parameters
John M. Campbell, Paul Levrie
Let be a hypergeometric function that may be expressed so that appears within initial arguments of inverted Pochhammer symbols, as in factors of the form $\frac{1}{(n)…
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…
New Clebsch-Gordan-type integrals involving threefold products of complete elliptic integrals
John M. Campbell
Multiple elliptic integrals related to the generalized Clebsch-Gordan (CG) integral are of importance in many areas in physics and special functions theory. Zhou has introduced and…
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…