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Perron's Formula

Perron's formula is given by

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds,

where

f(s)=suma_ne^(-lambda_ns).

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References

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.Hardy, G. H. and Riesz, M. The General Theory of Dirichlet's Series. New York: Dover, p. 12, 2005.

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Perron's Formula

Cite this as:

Weisstein, Eric W. "Perron's Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PerronsFormula.html

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