# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 2 Search : Fourier series
 complex Fourier series   سری ِ فوریه‌ی ِ همتافت   seri-ye Fourier-ye hamtâftFr.: série de Fourier complexe   The complex notation for the → Fourier series of a function f(x). Using → Euler's formulae, the function can be written in cimplex form as f(x) = Σ cn einx (summed from -∞ to ∞), where the → Fourier coefficients are cn = (1/2π)∫ f(x) e-inx dx (integral from -π to +π). Fourier series   سری ِ فوریه   seri-ye FourierFr.: séries Fourier   A mathematical tool used for decomposing a → periodic function into an infinite sum of sine and cosine functions. The general form of the Fourier series for a function f(x) with period 2π is: (1/2) a0 + Σ (an cos (nx) + bn sin (nx), summed from n = 1 to ∞, where an and bn are the → Fourier coefficients, measuring the strength of contribution from each harmonic. The functions cos (nx) and sin (nx) can be used in this way because they satisfy the → orthogonality conditions. For the problem of convergence of the Fourier series see → Dirichlet conditions. The Fourier series play a very important role in the study of periodic phenomena, because they allow one to decompose a large number of complex problems into simpler ones. The generalization of this method, called the → Fourier transform, makes it possible to also decompose non-periodic functions into harmonic components. See also → complex Fourier series, → Parseval's theorem.→ Fourier analysis; → series.