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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Hindawi Limited
2021
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oai:doaj.org-article:9efdff8ff4124245b2f26448144466c82021-11-22T01:11:13ZA Note on Derivative of Sine Series with Square Root1687-040910.1155/2021/7035776https://doaj.org/article/9efdff8ff4124245b2f26448144466c82021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7035776https://doaj.org/toc/1687-0409Chaundy 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.Sergiusz KęskaHindawi LimitedarticleMathematicsQA1-939ENAbstract and Applied Analysis, Vol 2021 (2021) |
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DOAJ |
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DOAJ |
| language |
EN |
| topic |
Mathematics QA1-939 |
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Mathematics QA1-939 Sergiusz Kęska A Note on Derivative of Sine Series with Square Root |
| description |
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. |
| format |
article |
| author |
Sergiusz Kęska |
| author_facet |
Sergiusz Kęska |
| author_sort |
Sergiusz Kęska |
| title |
A Note on Derivative of Sine Series with Square Root |
| title_short |
A Note on Derivative of Sine Series with Square Root |
| title_full |
A Note on Derivative of Sine Series with Square Root |
| title_fullStr |
A Note on Derivative of Sine Series with Square Root |
| title_full_unstemmed |
A Note on Derivative of Sine Series with Square Root |
| title_sort |
note on derivative of sine series with square root |
| publisher |
Hindawi Limited |
| publishDate |
2021 |
| url |
https://doaj.org/article/9efdff8ff4124245b2f26448144466c8 |
| work_keys_str_mv |
AT sergiuszkeska anoteonderivativeofsineserieswithsquareroot AT sergiuszkeska noteonderivativeofsineserieswithsquareroot |
| _version_ |
1718418297448300544 |