# Du Bois-Reymond criterion (convergence of series)

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 40A05 [MSN][ZBL]

A criterion for the convergence of series of complex numbers, established by P. du Bois-Reymond.

If the series of complex numbers $\sum_n b_n$ converges and the series of complex numbers $\sum_n (a_n-a_{n+1})$ converges absolutely, then the series $\sum_n a_n b_n$ converges.

#### References

[Kn] | K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990) |

**How to Cite This Entry:**

Du Bois-Reymond criterion (convergence of series).

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Du_Bois-Reymond_criterion_(convergence_of_series)&oldid=30930

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article