Perron formula
= Perron formula
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{wiki=Perron's_formula}
Perron's formula recovers a summatory arithmetic function from its <Dirichlet series> by the inverse Mellin integral
$$
\sum_{n\leq x}a_n
=\frac1{2\pi i}\int_{c-i\infty}^{c+i\infty}
\left(\sum_{n\geq1}\frac{a_n}{n^s}\right)\frac{x^s}{s}\,ds,
$$
with the usual convergence and endpoint conventions.