2019/01/07 by Patarroyo, Keith Y.
#33C45 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1901.01648
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite polynomials and show a few of their applications in the connection problem of polynomials, probability theory and the combinatorics of a simple graph. Most of the content presented here is well known, except for a few sections where we add our own work to the subject, nevertheless, the text is meant to be a self-contained personal exposition.