Cheon Seoung Ryoo

Hannam University

Dr. Cheon Seoung Ryoo is a professor of Mathematics at Hannam University, South Korea. He received his PhD in Mathematics from Kyushu University, Fukuoka, Japan. Dr. Ryoo is the author of several research articles on numerical computations with guaranteed accuracy. He has also contributed works to the fields of scientific computing, analytic number theory and p-adic functional analysis. More recently, he has been working with special functions, quantum calculus and differential equations.

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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.

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