# Parseval's theorem

From AMS Glossary

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## Parseval's theorem

A theorem relating the product of two functions to the products of their Fourier series components.

If the functions are There is an analogous theorem for Fourier transforms.

*f*(*x*) and*F*(*x*), and their Fourier series components have respective amplitudes*a*_{n},*b*_{n}and*A*_{n},*B*_{n}, Parseval's theorem states that under certain general conditions