• Corpus ID: 235367751

A Family of Bounded and Analytic Hyper-Operators

  title={A Family of Bounded and Analytic Hyper-Operators},
  author={J. Nixon},
  • J. Nixon
  • Published 28 May 2021
  • Mathematics
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 ↑ z : (1, e) × CR(z)>0 → CR(z)>0 using methods from fractional calculus. This family satisfies the hyper-operator chain, α ↑ α ↑ z = α ↑ (z + 1); with the initial condition… 


Dynamics in one complex variable
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large
Appendix. the Mellin Transform and Related Analytic Techniques
1. The generalized Mellin transformation The Mellin transformation is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics, such as the zeta
On The Indefinite Sum In Fractional Calculus
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We
Classical Topics in Complex Function Theory
An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician.
Hyper-operations By Unconventional Means arXiv
  • 2021
Ramanujan's Master
  • Theorem Ramanujan J
  • 2012
The Fractional Calculus
  • 2006