A Family of Bounded and Analytic HyperOperators
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 $\alpha \uparrow^n z : (1,e^{1/e}) \times \mathbb{C}_{\Re(z) > 0} \to \mathbb{C}_{\Re(z) > 0}$ using methods from fractional calculus. This family satisfies the hyperoperator chain, $\alpha \uparrow^{n1} \alpha \uparrow^n z = \alpha \uparrow^n (z+1)$; with the initial condition $\alpha \uparrow^0 z = \alpha \cdot z$.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2106.03935
 Bibcode:
 2021arXiv210603935N
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Dynamical Systems;
 30D05;
 30B50;
 37F10;
 39B12;
 39B32