Английская Википедия:Antilimit
Материал из Онлайн справочника
Шаблон:Unreferenced In mathematics, the antilimit is the equivalent of a limit for a divergent series. The concept not necessarily unique or well-defined, but the general idea is to find a formula for a series and then evaluate it outside its radius of convergence.
Common divergent series
| Series | Antilimit |
|---|---|
| 1 + 1 + 1 + 1 + ⋯ | -1/2 |
| 1 − 1 + 1 − 1 + ⋯ (Grandi's series) | 1/2 |
| 1 + 2 + 3 + 4 + ⋯ | -1/12 |
| 1 − 2 + 3 − 4 + ⋯ | 1/4 |
| 1 − 1 + 2 − 6 + 24 − 120 + … | 0.59634736... |
| 1 + 2 + 4 + 8 + ⋯ | -1 |
| 1 − 2 + 4 − 8 + ⋯ | 1/3 |
| 1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series) | - |
See also
- Abel summation
- Cesàro summation
- Lindelöf summation
- Euler summation
- Borel summation
- Mittag-Leffler summation
- Lambert summation
- Euler–Boole summation and Van Wijngaarden transformation can also be used on divergent series
References
