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ON THE BEHAVIOR NEAR THE ORIGIN OF THE SUM OF SINE SERIES WITH THIRD SEMI-CONVEX COEFFICIENTSKeywords: sine sums , third semi-convex null sequences , behavior near the origin. Abstract: In this paper we study the behavior of the sine series given byrelation:g(x) =1Xk=1ak sin kx;in case where x ! 0 and coecients (ak) are third semi-convex which tendingto zero.
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