- Trigonometric series
In
mathematics , a trigonometric series is any series of the form:: frac{1}{2}A_{o}+displaystylesum_{n=1}^{infty}(A_{n} cos{nx} + B_{n} sin{nx})."Fourier Series and Orthogonal Functions" By Harry F. Davis. Page 89]
It is called a
Fourier series when the terms A_{n} and B_{n} have the form::A_{n}=frac{1}{pi}displaystyleint^{2 pi}_0! f(x) cos{nx} ,dxqquad (n=0,1,2, dots)
:B_{n}=frac{1}{pi}displaystyleint^{2 pi}_0! f(x) sin{nx}, dxqquad (n=1,2,3, dots)
where f is an
integrable function ."Fourier Series and Orthogonal Functions" By Harry F. Davis. Page 89]It is not that case that every trigonometric series is a Fourier Series. A particular question of interest is given a trigonometric series, for which values of "x" does the series converge.
References
* "Trigonmetric Series" by A. Zygmund
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