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2 produkter
2 produkter
Häftad, Engelska, 2026
1 906 kr
Skickas inom 10-15 vardagar
Extended Hypergeometric Functions and Orthogonal Polynomials presents a comprehensive and accessible resource for researchers and graduate students interested in exploring the rich connections between extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials. Integrating all three fields and their applications in Maple, Mathematica, and MATLAB, this book fosters interdisciplinary understanding and inspires new avenues of research in mathematics, engineering, physics, and computer science. It also provides a glimpse into future research directions in these areas, including potential applications in emerging fields of applied mathematics and interdisciplinary collaborations. Each chapter begins with an introduction, includes sections on theory, followed by sections on applications, and ends with exercises, problems, references and suggested readings.Provides an integrated and up-to-date resource on extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials for researchers, students, and practicing engineersPresents emerging trends, new developments, techniques, and applications in the fields of special functions and orthogonal polynomialsGives special attention to practical techniques for working with these functions and polynomials, including computational methods and applications to solve real-world problems
Häftad, Engelska, 2026
848 kr
Kommande
This book presents a comprehensive and focused attempt to derive key properties of multidimensional, or multi-index, Chebyshev polynomials by using generalized Hermite polynomials as a foundational tool. It demonstrates how multi-index Hermite polynomials can be employed to construct multidimensional Chebyshev polynomials of both the first and second kinds. Through symbolic and integral techniques, including a formal treatment of the Laplace transform, the book investigates various generalizations of these polynomial families. Emphasizing multi-index formulations, it explores these polynomials through a symbolic framework involving suitable integral transforms by leveraging the Laplace transforms. Key operational techniques are developed and applied to deepen conceptual understanding and navigate the formal structures underpinning various derived relationships.The discussion is highlighted in applications inspired by real-world physical problems. Multi-index Hermite polynomials are examined in the context of quantum optics to model both coherent and incoherent radiation field distributions. Multidimensional systems coupled through electromagnetic radiation are addressed, alongside related wave propagation phenomena. Higher-order Laguerre polynomials are utilized to compute statistical moments of chaotic radiation, while multidimensional Bessel functions are explored for their role in laser theory. Traditional applications of Chebyshev polynomials in approximation theory are also revisited, providing a bridge between classic and contemporary mathematical approaches.The content of the book is designed into three parts, each addressing a distinct facet of the subject. Part I is devoted to the algebraic theory of general set-theoretic solutions to the Yang–Baxter equation, with particular emphasis on skew left braces and Rota–Baxter groups. Part II presents a detailed treatment of the algebraic theory of racks and quandles. Part III, the most advanced part of the book, is concerned with the homology and cohomology theories associated with solutions to the Yang–Baxter equation. From the point of view of logical dependency, Parts I and II are largely self-contained and may be read independently, while Part III builds upon foundational concepts introduced in the earlier parts.