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Westminster College Mathematics Major Interns at NIST, Has Paper Under Review

Posted on Monday, December 17, 2012

NEW WILMINGTON, Pa. - Westminster College junior mathematics major Connor MacKenzie interned at the National Institute of Standards and Technology (NIST) during the summer and currently has a paper under review for publication.

MacKenzie's main responsibilities at NIST were in a field of mathematics called special functions. He was asked by his NIST advisor to complete research on finding simplifications and generalizations of generating functions for classical orthogonal polynomials. The research resulted in two pending papers.

"Generalization and Simplifications of Generating Functions for Jacobi, Gegenbauer, Chebyshev and Legendre Polynomials with Definite Integrals" generalizes and simplifies generating functions for classical orthogonal polynomials by using a two element sequence of generating functions for Jacobi polynomials for some of the generalizations. The simplifications are done using formulas for general hypergeometric functions to express them as more elementary functions. He also uses orthogonality relations for his classical orthogonal polynomials to determine definite integrals.

Click here to read the paper.

He is still working on the second paper, which will review using connection relations to generalize more generating functions and also using orthogonality relations to determine more definite integrals.

MacKenzie's internship was through the Summer Undergraduate Research Fellowship (SURF) program in the Applied and Computational Mathematics Division (ACMD) of the Information Technology Laboratory at NIST. Westminster College nominated MacKenzie for the prestigious internship. In order to be accepted, NIST required transcripts, two letters of recommendation and a written personal statement from MacKenzie.

One highlight of MacKenzie's internship was to attend a presentation by a Nobel Prize winner.

"Every week we attended a talk, and one of them was from Nobel Laureate William Phillips. He gave a talk about the physics behind creating the most accurate clock. It was very fun to watch because he used a lot of liquid nitrogen in an explanation about how hard it was to get atoms cold enough in order to create more accurate time-keepers," Mackenzie said.

MacKenzie is grateful for the opportunities that came with the internship and knows that it prepared him for a life and career beyond the walls of Westminster, even if doesn't know exactly what type of career that might be.

"My goals after college are to go on to grad school and earn my doctorate. After that, I may pursue teaching in a college setting, but I might like to go into a more research-orientated career. Either way, this internship and the experience I gained are definitely helpful because I got to really see what it is like to be in a research atmosphere," MacKenzie said. "In writing my papers, I got experience in how mathematics is presented professionally, which will help for writing papers in the future, but will also help if I want to teach because I have experience of putting the complex ideas into understandable words."

MacKenzie is a son of Dwayne and Amy MacKenzie and a graduate of Ephrata High School.

Contact MacKenzie at for more information.

Connor MacKenzie,a junior mathematics major, interned at NIST during the summer.