E20 -- De summatione innumerabilium progressionum

(The summation of an innumerable progression)


This paper talks about z(2), denoted here s2= p2/6. This is about 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Then Euler brings in the harmonic series: let f(x) be the x-th partial sum of the harmonic series. Euler approximates this as an integral and defines his constant g as the limit of f(x)-log(x).

According to the records, it was presented to the St. Petersburg Academy on March 5, 1731.

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