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Number of Results: 2 Search : Fourier series

complex Fourier series seri-ye Fourier-ye hamtâft Fr.: série de Fourier complexe The complex notation for the → Fourier coefficients are
c (integral from -π to
+π)._{n} = (1/2π)∫ f(x) e^{-inx} dx→ |

Fourier series seri-ye Fourier Fr.: séries Fourier A mathematical tool used for decomposing a → a cos (_{n}nx) +
b sin (_{n}nx), summed from n = 1 to ∞, where a and _{n}b are the
→ _{n}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.→ |