Sharp Two-Sided Estimate for the Sum of a Sine Series with Convex Slowly Varying Sequence of Coefficients
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DOI: 10.1007/s10476-020-0047-5
Abstract: The sum of a sine series $$g\left({b,x} \right) = \sum\nolimits_{k = 1}^\infty {}$$ bk sin kx with coefficients forming a convex sequence b is known to be positive on the interval (0,π). To estimate its… read more here.
Keywords: left right; sine series; two sided; sum sine ... See more keywords
Asymptotics of the Sum of a Sine Series with a Convex Slowly Varying Sequence of Coefficients
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DOI: 10.3390/math9182252
Abstract: We study the asymptotic behavior in a neighborhood of zero of the sum of a sine series g(b,x)=∑k=1∞bksinkx whose coefficients constitute a convex slowly varying sequence b. The main term of the asymptotics of the… read more here.
Keywords: slowly varying; varying sequence; convex slowly; sum sine ... See more keywords