Bøger af Alma Adams

Orthogonal polynomials are a family of polynomials, wherein any two different polynomials in the sequence are orthogonal to each other under some inner product. Classical orthogonal polynomials, Hermite polynomials, Laguerre polynomials, Jacobi polynomials, and Gegenbauer polynomials are a few examples of orthogonal polynomials. These polynomials are used for least square approximations of a function, difference equations, and Fourier series. Another major application of orthogonal polynomials is error-correcting code and sphere packing. Orthogonal polynomials and special functions are useful mathematical functions, which have applications in various fields such as mathematical physics, statistics and probability, and engineering. These can be used to explain many physical and chemical phenomena. This book traces the recent studies in orthogonal polynomials and special functions. A number of latest researches have been included to keep the readers updated with the latest concepts in this area of study. With state-of-the-art inputs by acclaimed experts of mathematics, this book targets students and professionals.

A function containing several variables that remains unchanged for any permutation of the variables is called a symmetric function. Polynomials are a type of function. A symmetric polynomial refers to a type of polynomial P in n variables such that if any of the variables are swapped with each other, it remains the same polynomial. There are various types of symmetric polynomials including power-sum symmetric polynomials, elementary symmetric polynomials, complete homogeneous symmetric polynomials, monomial symmetric polynomials, and Schur polynomials. Symmetric polynomials have numerous applications in various areas of combinatorics, representation theory, mathematical physics, and mathematics. They are frequently found in Newton's identities and Vieta's formula. This book includes some of the vital pieces of works being conducted across the world, on various topics related to symmetric functions and polynomials, and their applications. It will serve as a valuable source of reference for graduate and postgraduate students.