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

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Included in

Mathematics Commons

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