PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 44(58), pp. 4964 (1988) 

ASYMPTOTIC BEHAVIOR OF PARTIAL SUMS OF FOURIERLEGENDRE SERIESR. Bojani\'c and Z. DivisDepartment of Mathematics, Ohio State University Columbus, Ohio 43210, USAAbstract: 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 FourierLegendre expansion of $f$: $$ S_n(f,x) = f(x)+(n\pi)^{1}\sqrt{1x^2}(f_R'(x)f_L'(x))+o(1/n). $$ Here $f_R'(x)$ and $f_L'(x)$ are the right and the left derivatives of $f$ at $x\in (1,1)$. Classification (MSC2000): 41A25, 42C10; 40A30 Full text of the article:
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