Summation of Powers over Product of Differences/Historical Note
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Historical Note on Summation of Powers over Product of Differences
The result Summation of Powers over Product of Differences was discussed by Leonhard Paul Euler in a letter to Christian Goldbach in $1762$.
He subsequently published it in his Institutiones Calculi Integralis, Volume 2 of $1769$.
The proof involving complex analysis was devised in $1857$ by James Joseph Sylvester.
Sources
- 1857: J.J. Sylvester: On a Discovery in the Partition of Numbers -- continued (Quart. J. Pure Appl. Math. Vol. 1: pp. 141 – 152)
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products: Exercise $33$