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arXiv · 2106.03935

A Family of Bounded and Analytic Hyper-Operators

James David Nixon
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Abstract

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 and disorganized; the author decided to rewrite the cumulative research. The goal of this paper is to construct a family of analytic functions $α\uparrow^n z : (1,e^{1/e}) \times \mathbb{C}_{\Re(z) > 0} \to \mathbb{C}_{\Re(z) > 0}$ using methods from fractional calculus. This family satisfies the hyper-operator chain, $α\uparrow^{n-1} α\uparrow^n z = α\uparrow^n (z+1)$; with the initial condition $α\uparrow^0 z = α\cdot z$.

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James David Nixon. 2021-05-28. A Family of Bounded and Analytic Hyper-Operators. https://arxiv.org/abs/2106.03935

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