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Reference.org
Generalized Fourier series
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<p>A generalized Fourier series is the expansion of a <a href="/facts/Square_integrable/IASblcJJ">square integrable</a> function into a sum of square integrable <a href="/facts/Orthogonal_basis/H4DgNCgR"> orthogonal basis functions</a>. The standard <a href="/facts/Fourier_series/s3fsxPAT">Fourier series</a> uses an <a href="/facts/Orthonormal_basis/pzfKHlJG">orthonormal basis</a> of <a href="/facts/Trigonometric_functions/czej7ur0">trigonometric functions</a>, and the series expansion is applied to periodic functions. In contrast, a generalized Fourier series uses any set of orthogonal basis functions and can apply to any <a href="/facts/Square-integrable_function/IASblcJJ">square integrable function</a>. </p>