Summation of Powers over Product of Differences/Historical Note

Historical Note on Summation of Powers over Product of Differences
The result Summation of Powers over Product of Differences was discussed by in a letter to  in $1762$.

He subsequently published it in his of $1769$.

The proof involving complex analysis was devised in $1857$ by.

The Example according to in his  is the discovery of fictitious character Dr Matrix.