Ermakov convergence criterion

for a series with positive numbers as terms

Let be a positive decreasing function for . If the inequality

holds for these values of with a , then the series

converges; if

then the series diverges. In particular, if the following limit exists and

then the series converges (diverges). This criterion was established by V.P. Ermakov [1].

References

[1]	V.P. Ermakov, "A new criterion for convergence and divergence of infinite series of constant sign" , Kiev (1872) (In Russian)

References

[a1]	T.J. Bromwich, "An introduction to the theory of infinite series" , Macmillan (1947)

How to Cite This Entry:
Ermakov convergence criterion. L.D. Kudryavtsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Ermakov_convergence_criterion&oldid=16787

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098