This article discusses the fundamental concepts of Fourier series theory, its mathematical formulation, and practical applications. It is shown that periodic functions can be represented as a sum of sine and cosine functions. The paper analyzes the methods for determining Fourier coefficients, the convergence conditions of the series, and its applications in physics and engineering. The results highlight the significant role of Fourier series in mathematical analysis, signal processing, and the study of oscillatory processes.

Fourier series, periodic function, sine and cosine, Fourier coefficients, convergence, mathematical analysis, signal processing.

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