A Note on Derivative of Sine Series with Square Root
Chaundy and Jolliffe proved that if an is a nonnegative, nonincreasing real sequence, then series ∑ansinnx 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...
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| Formato: | article |
| Lenguaje: | EN |
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Hindawi Limited
2021
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| Acceso en línea: | https://doaj.org/article/9efdff8ff4124245b2f26448144466c8 |
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| Sumario: | Chaundy and Jolliffe proved that if an is a nonnegative, nonincreasing real sequence, then series ∑ansinnx 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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