Optimal rate of convergence for sequences of a prescribed form. (English) Zbl 1323.40003
Summary: We provide a highly convergent version of the generalized Euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form.
The new approach extends and unifies many previous efforts in this direction. In addition, we answer an open problem on the asymptotic expansion of the harmonic number sequence.
The new approach extends and unifies many previous efforts in this direction. In addition, we answer an open problem on the asymptotic expansion of the harmonic number sequence.
MSC:
| 40A25 | Approximation to limiting values (summation of series, etc.) |
| 11Y60 | Evaluation of number-theoretic constants |
| 33B15 | Gamma, beta and polygamma functions |
| 65B15 | Euler-Maclaurin formula in numerical analysis |
