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Dirichlet-Hardy Test


If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then sum_(r=1)^(n)a_r(x)v_r is uniformly convergent in the interval.


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References

Jeffreys, H. and Jeffreys, B. S. "Dirichlet-Hardy Test." §1.1155 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 42-43, 1988.

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Dirichlet-Hardy Test

Cite this as:

Weisstein, Eric W. "Dirichlet-Hardy Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Dirichlet-HardyTest.html

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