Euler-Fourier Formulas

formulas for calculating the coefficients of the expansion of a function in a trigonometric series (Fourier series). The Euler-Fourier formulas are named after L. Euler, who provided their first derivation in 1777, and J. Fourier, who, beginning in 1811, systematically used trigonometric series in the study of problems of heat conduction. (SeeFOURIER COEFFICIENT and TRIGONOMETRIC SERIES.)