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A Note on Derivative of Sine Series with Square Root

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  • Sergiusz Kęska

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.

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Handle: RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:7035776
DOI: 10.1155/2021/7035776
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