Question

State and prove Parseval's identity for Fourier series.​

Answer 1

Answer:

• In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is a generalised Pythagorean theorem for inner-product spaces (which can have an uncountable infinity of basis vectors).

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Answer 2

Answer:

• In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is a generalised Pythagorean theorem for inner-product spaces (which can have an uncountable infinity of basis vectors).