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'Parseval equality'
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| Title of object: |
Parseval equality |
| Canonical Name: |
PersevalEquality |
| Type: |
Theorem |
| Created on: |
2003-09-10 10:05:39 |
| Modified on: |
2007-08-10 23:18:52 |
| Classification: |
msc:42B05 |
| Synonyms: |
Parseval equality=Parseval theorem
Parseval equality=Parseval equation |
Revision comment (for changes between this and next version):
| Changes for correction #13060 ('general version'). |
Preamble:
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%\usepackage{psfrag}
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Content:
Let $f$ be a Riemann integrable function from $[-\pi,\pi]$ to $R$. The equation
$$\frac{1}{\pi}\int_{-\pi}^{\pi}f^2(x)dx = \frac{(a_0^f)^2}{2} + \sum_{k=1}^{\infty}[(a_k^f)^2+(b_k^f)^2],$$
where $a_0^f$, $a_k^f$, $b_k^f$ are the Fourier coefficients of the function $f$, is usually known as Parseval's equality or Parseval's theorem. |
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