Parseval Equality

an equation of the form

where a₀ a_n, and b_n are the Fourier coefficients for f(x). It was established in 1805 by the French mathematician M. Parseval by assuming that trigonometric series could be termwise integrated. In 1896, A. M. Liapunov showed that the equality is valid if the function is bounded on the interval (—π, π) and if the integral ∫^π_-πf(x) dx exists. It was later proved that the Parseval equality holds for any function whose square is integrable. V. A. Steklov demonstrated that the Parseval equality is valid for series in other orthogonal systems of functions.

单词	parseval equality
释义	Parseval Equality Parseval Equality an equation of the form where a₀ a_n, and b_n are the Fourier coefficients for f(x). It was established in 1805 by the French mathematician M. Parseval by assuming that trigonometric series could be termwise integrated. In 1896, A. M. Liapunov showed that the equality is valid if the function is bounded on the interval (—π, π) and if the integral ∫^π_-πf(x) dx exists. It was later proved that the Parseval equality holds for any function whose square is integrable. V. A. Steklov demonstrated that the Parseval equality is valid for series in other orthogonal systems of functions.
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