E477 -- Meditationes circa singulare serierum genus

(Meditations about a singular type of series)


Summary:

Euler shows that sm, n = 1 + (1/2m)(1 + 1/2n) + (1/3m)(1 + 1/2n + 1/3n) + (1/4m)(1 + 1/2n + 1/3n + 1/4n) + ... and sn = sn, 0. He gets a relation sn, n = sn2 + s2n, along with some similar, more complicated formulas. Then he evaluates sm, n for m + n = 6.

According to the records, it was presented to the St. Petersburg Academy on July 4, 1771.

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