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Divergent Series
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Geliefert zwischen Mi., 04.02.2026 und Do., 05.02.2026
Details
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit. If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms do not approach zero diverges. However, convergence is a stronger condition: not all series whose terms approach zero converge. The simplest counter example is the harmonic series A summability method M is regular if it agrees with the actual limit on all convergent series. Such a result is called an abelian theorem for M, from the prototypical Abel's theorem. More interesting and in general more subtle are partial converse results, called tauberian theorems, from a prototype proved by Alfred Tauber. Here partial converse means that if M sums the series , and some side-condition holds, then was convergent in the first place; without any side condition such a result would say that M only summed convergent series (making it useless as a summation method for divergent series).
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131107313
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131107313
- Format Fachbuch
- Titel Divergent Series
- Herausgeber Betascript Publishing
- Anzahl Seiten 100
- Genre Mathematik
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