Geodesic
Asymptotic Behavior of Partial Sums of Fourier-Legendre Series
Publications de l'Institut Mathématique, _N_S_44 (1988) no. 58, p. 49

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If $f$ is defined and has a derivative of bounded variation on $[-1,1]$ the main result of this paper is the asymptotic formula for the partial sums of the Fourier-Legendre expansion of $f$: $ S_n(f,x) = f(x)+(n\pi)^{-1}\sqrt{1-x^2}(f_R'(x)-f_L'(x))+o(1/n). $ Here $f_R'(x)$ and $f_L'(x)$ are the right and the left derivatives of $f$ at $x\in (-1,1)$.
Classification : 41A25 42C10 40A30 
@article{PIM_1988_N_S_44_58_a7,
     author = {R. Bojani\'c and Z. Divis},
     title = {Asymptotic {Behavior} of {Partial} {Sums} of {Fourier-Legendre} {Series}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {49 },
     publisher = {mathdoc},
     volume = {_N_S_44},
     number = {58},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1988_N_S_44_58_a7/}
}
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R. Bojanić; Z. Divis. Asymptotic Behavior of Partial Sums of Fourier-Legendre Series. Publications de l'Institut Mathématique, _N_S_44 (1988) no. 58, p. 49 . http://geodesic.mathdoc.fr/item/PIM_1988_N_S_44_58_a7/