Sequences that converge to a generalization of Ioachimescu’s constant. (English) Zbl 1265.40014
Summary: We consider a generalization of Ioachimescu’s constant as the limit \(\mathcal I(a;s)\) of the sequence \(\left(\frac 1{a^s} +\frac 1{(a+1)^s} +...+\frac 1{(a+n-1)^s}-\frac 1{1-s} ((a+n-1)^{1-s}-a^{1-s})\right)_{n\in\mathbb N}\), where \(a\in (0,+\infty)\) and \(s\in (0,1)\).
The purpose of this paper is to give some sequences that converge quickly to \(\mathcal I(a;s)\).
The purpose of this paper is to give some sequences that converge quickly to \(\mathcal I(a;s)\).
MSC:
| 40A25 | Approximation to limiting values (summation of series, etc.) |
| 11Y60 | Evaluation of number-theoretic constants |
