Date of Award
4-20-2017
Document Type
Thesis
Degree Name
Mathematics, MS
First Advisor
William Paulsen
Committee Members
Jeongho Ahn; Jie Miao
Call Number
LD251 .A566t 2017 C69
Abstract
We will look at the tetration problem for when the bases satisfy b > e^{1/e}. We will prove that Knesser’s solution is the unique true solution to the tetration equation F(x+1)=g(F(x)), where g(x) = b^x. After proving this uniqueness, a new iteration method is developed and will give way to the development of the arctetration function. We will use the complex Fourier series coefficients and the Cauchy-Integral formula aided with Gaussian quadrature with only 180 nodes, to numerically evaluate this solution, which improves the number of calculation iterations from previous methods. This thesis will also look at the next level which is known as pentation and we will also look at fractional iterates, such as the half-iterate, which satisfies f(f(x))=b^x.
Rights Management
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Cowgill, Samuel Patrick, "Exploring Tetration in the Complex Plane" (2017). Student Theses and Dissertations. 562.
https://arch.astate.edu/all-etd/562
