| RefNo | PP/1/3 |
| Previous numbers | PP/33/3 |
| Level | Item |
| Title | Paper, 'The sums of the series of the reciprocals of the prime numbers and of their powers' by C W [Charles Watkins] Merrifield |
| 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'. |
| Extent | 10p |
| Format | Manuscript |
| PhysicalDescription | Ink and graphite pencil on paper |
| Digital images | View item on Science in the Making |
| AccessStatus | Open |
| RelatedMaterial | DOI: 10.1098/rspl.1881.0063 |
Fellows associated with this archive
| Code | PersonName | Dates |
| NA729 | Merrifield; Charles Watkins (1827 - 1884) | 1827 - 1884 |