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Ermakov convergence criterion

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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)


Comments

References

[a1] T.J. Bromwich, "An introduction to the theory of infinite series" , Macmillan (1947)
How to Cite This Entry:
Ermakov convergence criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ermakov_convergence_criterion&oldid=16787
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article