Discipline: Mathematics and Statistics
Hydeia Bailey - Savannah State University
This research paper will explain the history of Legendre Polynomials and their connection with Legendre differential equations. The Legendre differential equation will be solved to obtain the Legendre Polynomials. The first few Legendre polynomials will be listed and an illustration of the graph will be shown. Some properties associated with Legendre polynomials will be discussed. We will also present the zeros of some of the polynomials. The discussion of the zeros/roots will lead to how the Legendre Polynomials are used to solve Gauss-Legendre Integration. Some examples of the Gauss-Legendre quadrature will be presented.
Funder Acknowledgement(s): Chellu Chetty and HBCU-UP
Faculty Advisor: Agegnehu Atena, Atenaa@savannahstate.edu
Role: I was in charge of researching and studying the mathematical topic. I also was in charge of typing the research essay.