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Paper, 'The sums of the series of the reciprocals of the prime numbers and of their powers' by C W [Charles Watkins] Merrifield

Reference number: PP/1/3

Date: 1881

Description

Merrifield writes 'Euler has shown that it is possible to sum the series of reciprocals of powers of the prime numbers, and he has calculated the values of these sums for the even powers. I thought it of some interest to calculate the sums for the odd powers, and to evaluate a peculiar constant (somewhat analogous to the Eulerian constant,— γ = 0·57721 56649 01532 86060 65) which presents itself, in the series of simple reciprocals of primes, as the difference between the sum of the series and the double logarithmic infinity to the Napierian base ϵ. The summation of these series was shown by Euler to depend upon the Napierian logarithms of the sums of the reciprocals of the powers of the natural numbers.'

Annotations in pencil.

Subject: Mathematics

Received 8 August 1881. Read 17 November 1881.

A version of this paper was published in volume 33 of the Proceedings of the Royal Society as 'The sums of the series of the reciprocals of the prime numbers and of their powers'.

Reference number
PP/1/3
Earliest possible date
1881
Physical description
Ink and graphite pencil on paper
Page extent
10 pages
Format
Manuscript

Creator name

Charles Watkins Merrifield

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Citation

Charles Watkins Merrifield, Paper, 'The sums of the series of the reciprocals of the prime numbers and of their powers' by C W [Charles Watkins] Merrifield, 1881, PP/1/3, The Royal Society Archives, London, https://makingscience.royalsociety.org/items/pp_1_3/paper-the-sums-of-the-series-of-the-reciprocals-of-the-prime-numbers-and-of-their-powers-by-c-w-charles-watkins-merrifield, accessed on 24 June 2024

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  • Proceedings Papers

    Dates: 1882 - 1894

    The archival collection known as 'Proceedings Papers' is comprised of manuscripts and occasional proofs of scientific papers sent to the Royal Society which were read before meetings of Fellows and printed in full in the Proceedings of the Royal Society.

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