A Note on Derivative of Sine Series with Square Root

Sergiusz Kęska

Abstract and Applied Analysis, 2021, vol. 2021, issue 1

Abstract: Chaundy and Jolliffe proved that if {an} is a nonnegative, nonincreasing real sequence, then series ∑ansin(nx) converges uniformly if and only if nan⟶0. The purpose of this paper is to show that if {nan} is nonincreasing and nan⟶0, then the series fx=∑ansinnx can be differentiated term‐by‐term on [c, d] for c, d > 0. However, f′(0) may not exist.

Date: 2021
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https://doi.org/10.1155/2021/7035776

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:7035776

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