Name
Abstract | ||
|---|---|---|
Let γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove that for all integers n≥1, 124(n+a)2≤Rn−γ<124(n+b)2 with the best possible constants a=124[−γ+1−log(3/2)]−1=0.55106…andb=12. This refines the result of D. W. DeTemple, who proved that the double inequality holds with a=1 and b=0. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.aml.2009.09.005 | Applied Mathematics Letters |
Keywords | Field | DocType |
Euler’s constant,Harmonic numbers,Inequality,Psi function,Asymptotic expansion | Integer,Mathematical optimization,Mathematical analysis,Harmonic number,Asymptotic expansion,Mathematics,Euler–Mascheroni constant | Journal |
Volume | Issue | ISSN |
23 | 2 | 0893-9659 |
Citations | PageRank | References |
10 | 1.35 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chao-Ping Chen | 1 | 58 | 12.24 |