Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials
Descartes' rule of signs
obtaining explicit formulas and identities for polynomials defined by generating functions
polynomials with symmetric zeros
numerical investigation on the structure of the zeros of the q-tangent polynomials
investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory
pricing basket options by polynomial approximations
and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.