Notes on a General Sequence
Let {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2020-09-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/amsil.2020.34.issue-2/amsil-2020-0006/amsil-2020-0006.xml?format=INT |
| _version_ | 1818559015289880576 |
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| author | Farhadian Reza Jakimczuk Rafael |
| author_facet | Farhadian Reza Jakimczuk Rafael |
| author_sort | Farhadian Reza |
| collection | DOAJ |
| description | Let {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and limits for the counting function of this sequence. All of the results are applied to some well-known sequences in mathematics. |
| first_indexed | 2024-12-14T00:19:51Z |
| format | Article |
| id | doaj.art-7ddb8c6c39dc4bcca47be5c3aab67bf6 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-12-14T00:19:51Z |
| publishDate | 2020-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-7ddb8c6c39dc4bcca47be5c3aab67bf62022-12-21T23:25:17ZengSciendoAnnales Mathematicae Silesianae2391-42382020-09-0134219320210.2478/amsil-2020-0006amsil-2020-0006Notes on a General SequenceFarhadian Reza0Jakimczuk Rafael1Department of Statistics, Lorestan University, KhorramabadIranDivisión Matemática, Universidad Nacional de Luján, Luján, Buenos Aires, RepúblicaArgentinaLet {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and limits for the counting function of this sequence. All of the results are applied to some well-known sequences in mathematics.http://www.degruyter.com/view/j/amsil.2020.34.issue-2/amsil-2020-0006/amsil-2020-0006.xml?format=INTgeneral sequenceasymptotic formulaelimit behaviorthe number e97i3011k3111b8340a0511b39 |
| spellingShingle | Farhadian Reza Jakimczuk Rafael Notes on a General Sequence Annales Mathematicae Silesianae general sequence asymptotic formulae limit behavior the number e 97i30 11k31 11b83 40a05 11b39 |
| title | Notes on a General Sequence |
| title_full | Notes on a General Sequence |
| title_fullStr | Notes on a General Sequence |
| title_full_unstemmed | Notes on a General Sequence |
| title_short | Notes on a General Sequence |
| title_sort | notes on a general sequence |
| topic | general sequence asymptotic formulae limit behavior the number e 97i30 11k31 11b83 40a05 11b39 |
| url | http://www.degruyter.com/view/j/amsil.2020.34.issue-2/amsil-2020-0006/amsil-2020-0006.xml?format=INT |
| work_keys_str_mv | AT farhadianreza notesonageneralsequence AT jakimczukrafael notesonageneralsequence |