Classical and Quantum Orthogonal Polynomials in One Variable

Mourad E. H. Ismail presents a comprehensive exploration of orthogonal polynomials, bridging classical theories and quantum perspectives. This work serves as a critical resource for mathematicians, physicists, and researchers, unraveling the intricate connections between different polynomial families within a unified framework. The author delves into both the historical context and contemporary applications, offering readers an extensive overview of this specialized field.

The discussion begins with foundational principles, setting the stage for a deeper understanding of the subject. Ismail skillfully illustrates how classical polynomials emerge from essential mathematical theories, before transitioning to novel quantum interpretations. Each chapter systematically addresses key concepts, ensuring clarity and accessibility for both novices and experienced practitioners.

Key applications of these polynomials in various scientific domains are highlighted, emphasizing their significance in solving differential equations and quantum mechanics. The text not only serves as an academic reference but also inspires new avenues for research and inquiry within the world of mathematics.

With its blend of thoroughness and clarity, this volume is poised to become an indispensable reference for anyone interested in the evolving landscape of orthogonal polynomials, making complex ideas approachable while maintaining scholarly rigor.