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Ermakoff's Test

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if

lim_(x->infty)^_(e^xf(e^x))/(f(x))<1

and divergent if

lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

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References

Bromwich, T. J. I'A. and MacRobert, T. M. An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 43, 1991.

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Ermakoff's Test

Cite this as:

Weisstein, Eric W. "Ermakoff's Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ErmakoffsTest.html

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