The Period of the Coefficients of the Gaussian Polynomial[N+33]

Author

Arturo J. Martinez, The University of Texas Rio Grande Valley

Date of Award

8-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Brandt Kronholm

Second Advisor

Dr. Jacob White

Third Advisor

Dr. Timothy Huber

Abstract

Definition 1. For any N, the central coefficient(s) of [N+33] is denoted by C0(N) and the coefficient that is x ''away" from the central coefficient(s) of [N+33] is denoted by Cx(N).

In [1] the following result is proved:

Theorem 2. The central coefficient(s) of the Gaussian polynomial [N+33] are described by the generating function

[Special characters omitted]

This generating function has period 4.

The main goal of this thesis is to generalize Theorem 0.2 by way of proving the following conjecture:

Conjecture 3. For any x the generating function for Cx(N) has period 4 and is given in three cases:

[Special characters omitted]

Comments

Copyright 2020 Arturo J. Martinez. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/period-coefficients-gaussian-polynomial-sup-n-3/docview/2520963455/se-2?accountid=7119

Recommended Citation

Martinez, Arturo J., "The Period of the Coefficients of the Gaussian Polynomial[N+33]" (2020). Theses and Dissertations. 716.
https://scholarworks.utrgv.edu/etd/716