Important Results on Polynomials

Abstract

Polynomials play a central role in algebra, analysis, number theory, and applied mathematics. This thesis presents a concise overview of several fundamental results that characterize their behavior and structure. This thesis focuses on the study and analysis of special classes of polynomials, which are Bernoulli polynomials, Bell polynomials, p-Bell polynomials, r-Bell polynomials, partial Bell polynomials, and complete Bell polynomials. We present their generating functions, explicit expressions, recurrence relations, and their relationships with Stirling numbers