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Perron's formula : ウィキペディア英語版 | Perron's formula In mathematics, and more particularly in analytic number theory, Perron's formula is a formula due to Oskar Perron to calculate the sum of an arithmetical function, by means of an inverse Mellin transform. ==Statement== Let be an arithmetic function, and let : Here, the prime on the summation indicates that the last term of the sum must be multiplied by 1/2 when ''x'' is an integer. The integral is not a convergent Lebesgue integral, it is understood as the Cauchy principal value. The formula requires ''c'' > 0, ''c'' > σ, and ''x'' > 0 real, but otherwise arbitrary.
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