BESSEL FUNCTIONS AND BESSEL-FOURIER SERIES: THEORETICAL BASIS, HISTORICAL DEVELOPMENT, AND PRACTICAL APPLICATIONS

This article comprehensively analyzes the theoretical foundations, historical development, and applications of Bessel functions and Bessel-Fourier series in modern mathematics and technology. Starting from historical sources, based on the scientific works of classical and modern scientists and the results of practical research, the significance of Bessel functions, their applications in differential equations and physical processes, as well as the analytical and computational capabilities of Bessel-Fourier series are studied in depth. The article also presents methodological discussions and critical analyses.