A Comprehensive Exploration of Orthogonal Polynomials in Classical and Contemporary Mathematical Analysis

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Dr. Abhijit Sen

A Comprehensive Exploration of Orthogonal Polynomials in Classical and Contemporary Mathematical Analysis

Authors: Dr. Abhijit Sen

Unique Paper ID: 182615
Volume: 4
Issue: 4
PageNo: 392-399

Keywords: Orthogonal polynomials numerical analysis spectral methods approximation theory random matrix theory.

Abstract:
Orthogonal polynomials play a pivotal role in mathematical analysis, seamlessly connecting classical methodologies with modern applications in numerical methods, approximation theory and computational sciences. This review article consolidates the theoretical foundations, classical polynomial families and recent advancements in orthogonal polynomials. It examines key properties, including orthogonality, recurrence relations and generating functions, while highlighting their critical roles in solving differential equations, developing quadrature rules and advancing spectral methods. The versatility of orthogonal polynomials is showcased through their applications in physics, signal processing and random matrix theory, with emphasis on computational and theoretical developments. This article provides a clear and accessible overview for researchers and practitioners, underscoring the precision of polynomials in modeling complex systems and their computational efficiency. It also explores interdisciplinary applications and emerging research trends, affirming their continued relevance in mathematical innovation.

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Cite This Article

ISSN: 2349-6002
Volume: 4
Issue: 4
PageNo: 392-399

A Comprehensive Exploration of Orthogonal Polynomials in Classical and Contemporary Mathematical Analysis

Available:https://ijirt.org/Article?manuscript=182615

07 Jul, 2025

Physics Phenomenology: Bridging Theory and Experiment in Modern Physics

Impact Factor
8.01 (Year 2024)

UGC Approved
Journal no 47859

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