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Fejes Tóth's Integral


\begin{displaymath}
{1\over 2\pi(n+1)} \int_{-\pi}^\pi f(x)\left\{{\sin[{\textst...
...er 2}}(n+1)x]\over\sin({\textstyle{1\over 2}}x)}\right\}^2\,dx
\end{displaymath}

gives the $n$th Cesàro Mean of the Fourier Series of $f(x)$.


References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 12, 1975.




© 1996-9 Eric W. Weisstein
1999-05-26