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Cross-references: Riemann integral, place, Lebesgue integral, function, Fourier coefficients, trigonometric functions, interval, integrable functions, square, orthonormal set, difference, inequality, Bessel's inequality, equality, Hilbert space, orthonormal basis
There are 10 references to this entry.
This is version 8 of Parseval equality, born on 2003-09-10, modified 2008-09-07.
Object id is 4717, canonical name is PersevalEquality.
Accessed 11622 times total.
Classification:
| AMS MSC: | 42B05 (Fourier analysis :: Fourier analysis in several variables :: Fourier series and coefficients) |
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Pending Errata and Addenda
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![$ L^2([-\pi,\pi])$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img6.png "$ L^2([-\pi,\pi])$"){kind=small}
![$ [-\pi,\pi]$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img7.png "$ [-\pi,\pi]$"){kind=small}
![$ [-\pi,\pi]$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img9.png "$ [-\pi,\pi]$"){kind=small}
![$\displaystyle \frac{1}{\pi}\int_{-\pi}^{\pi}f^2(x)dx = \frac{(a_0^f)^2}{2} + \sum_{k=1}^{\infty}[(a_k^f)^2+(b_k^f)^2],$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img11.png "$\displaystyle \frac{1}{\pi}\int_{-\pi}^{\pi}f^2(x)dx = \frac{(a_0^f)^2}{2} + \sum_{k=1}^{\infty}[(a_k^f)^2+(b_k^f)^2],$")
