Fejes Tóth's Integral

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

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.