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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/7035776 |
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| _version_ | 1850179363286286336 |
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| author | Sergiusz Kęska |
| author_facet | Sergiusz Kęska |
| author_sort | Sergiusz Kęska |
| collection | DOAJ |
| 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 |
| id | doaj-art-9efdff8ff4124245b2f26448144466c8 |
| institution | OA Journals |
| issn | 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9efdff8ff4124245b2f26448144466c82025-08-20T02:18:32ZengWileyAbstract and Applied Analysis1687-04092021-01-01202110.1155/2021/7035776A Note on Derivative of Sine Series with Square RootSergiusz Kęska0Faculty of Exact and Natural SciencesChaundy 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.http://dx.doi.org/10.1155/2021/7035776 |
| spellingShingle | Sergiusz Kęska A Note on Derivative of Sine Series with Square Root Abstract and Applied Analysis |
| title | 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_short | A Note on Derivative of Sine Series with Square Root |
| title_sort | note on derivative of sine series with square root |
| url | http://dx.doi.org/10.1155/2021/7035776 |
| work_keys_str_mv | AT sergiuszkeska anoteonderivativeofsineserieswithsquareroot AT sergiuszkeska noteonderivativeofsineserieswithsquareroot |