2 citations · 11 across the 13 of their papers we have counts for
5 papers · 2 filters
Infinite Compositions and Complex Dynamics; Generalizing Schröder and Abel Functions
James David Nixon
Using infinite compositions, we solve the general equations for holomorphic functions and . We describe the situations in which this equation is palpab…
The Limits of a Family; of Asymptotic Solutions to The Tetration Equation
James David Nixon
In this paper we construct a family of holomorphic functions which are solutions to the asymptotic tetration equation. Each satisfies the functional relationship ${\…
A Family of Bounded and Analytic Hyper-Operators
James David Nixon
This is a summation of research done in the author's second and third year of undergraduate mathematics at The University of Toronto. As the previous details were largely scattered…
Second Order Transfer Equations; and Generalizations to Arbitrary Orders
James David Nixon
The author provides a solution to the equation ; where is holomorphic; and is a holomorphic function wi…
Hyper-operations By Unconventional Means
James David Nixon
The author makes use of infinite compositions and a limiting function to construct a tetration function $\mathcal{F}(t) = e \tet t$. As a tetration function, $…