2 citations · 11 across the 13 of their papers we have counts for
13 papers
Asymptotic Solutions of the Tetration Equation
James David Nixon
In this report we construct a family of holomorphic functions which behave asymptotically like iterated exponentials as in the right half plane. Each…
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, $…
The Compositional Integral: The Narrow And The Complex Looking-Glass
James David Nixon
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogu…
The Compositional Integral: A Brief Introduction
James David Nixon
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way…
or: How I Learned to Stop Worrying and Love the -function
James David Nixon
For a nice holomorphic function in two variables, a respective holomorphic Gamma function is constructed, such that . Along the way, we fa…
The Bounded Analytic Hyper-operators
James D. Nixon
In a previous paper \cite{ref1} we produced a sequence of analytic functions when and was in the right half of the complex…
Complex Iterations of Entire Functions
James D. Nixon
In a previous paper we produced a complex iteration of a holomorphic function in the immediate basin of a fixed point whose multiplier is a real number and in between zero and…
On The Indefinite Sum In Fractional Calculus
James Nixon
We present a theorem on taking the repeated indefinite summation of a holomorphic function in a vertical strip of satisfying exponential bounds as the imaginary…
Complex Iterations and Bounded Analytic Hyper-operators
James Nixon
We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holom…