Euler's constant, sequences and some estimates
We give a class of sequences with the argument of the logarithmic term modified and that converge quickly to a generalization of Euler's constant denoted by γ(a), i.e. the limit of the sequence (∑k=1n1/(a+k-1)-ln((a+n-1)/a)n∈ℕ, where a∈(0,+∞). Also, we obtain estimates for γ-(∑k=1n1/k-ln(n+1/...
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University Constantin Brancusi of Targu-Jiu
2013-12-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | http://www.utgjiu.ro/math/sma/v08/p09.pdf |
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doaj-867fc1bb4a374735ab2ed6d97c17d5d62020-11-24T22:30:18ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982013-12-018 (2013)103114Euler's constant, sequences and some estimatesAlina Sîntămărian0Department of Mathematics,Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania We give a class of sequences with the argument of the logarithmic term modified and that converge quickly to a generalization of Euler's constant denoted by γ(a), i.e. the limit of the sequence (∑k=1n1/(a+k-1)-ln((a+n-1)/a)n∈ℕ, where a∈(0,+∞). Also, we obtain estimates for γ-(∑k=1n1/k-ln(n+1/2+1/(24(n+1/2)))), where γ=γ(1) is the Euler's constant. http://www.utgjiu.ro/math/sma/v08/p09.pdfSequenceConvergenceApproximationEuler's constantBernoulli numberEstimate |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alina Sîntămărian |
| spellingShingle |
Alina Sîntămărian Euler's constant, sequences and some estimates Surveys in Mathematics and its Applications Sequence Convergence Approximation Euler's constant Bernoulli number Estimate |
| author_facet |
Alina Sîntămărian |
| author_sort |
Alina Sîntămărian |
| title |
Euler's constant, sequences and some estimates |
| title_short |
Euler's constant, sequences and some estimates |
| title_full |
Euler's constant, sequences and some estimates |
| title_fullStr |
Euler's constant, sequences and some estimates |
| title_full_unstemmed |
Euler's constant, sequences and some estimates |
| title_sort |
euler's constant, sequences and some estimates |
| publisher |
University Constantin Brancusi of Targu-Jiu |
| series |
Surveys in Mathematics and its Applications |
| issn |
1843-7265 1842-6298 |
| publishDate |
2013-12-01 |
| description |
We give a class of sequences with the argument of the logarithmic term modified and that converge quickly to a generalization of Euler's constant denoted by γ(a), i.e. the limit of the sequence (∑k=1n1/(a+k-1)-ln((a+n-1)/a)n∈ℕ, where a∈(0,+∞).
Also, we obtain estimates for γ-(∑k=1n1/k-ln(n+1/2+1/(24(n+1/2)))), where γ=γ(1) is the Euler's constant. |
| topic |
Sequence Convergence Approximation Euler's constant Bernoulli number Estimate |
| url |
http://www.utgjiu.ro/math/sma/v08/p09.pdf |
| work_keys_str_mv |
AT alinasintamarian eulersconstantsequencesandsomeestimates |
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1725741662577098752 |