E130 -- De seriebus quibusdam considerationes

(Considerations on certain series)


Euler factors a power series into an infinite product, applying it to f'/f, and he evaluates a number of series that look like trigonometric substitutions. He also applies this to the differential equation zs' - s - sz + s2 = 0 by recursion. Then he takes a shot at z(2k+1).

According to the records, it was presented to the St. Petersburg Academy on October 22, 1739.

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