E489 -- De formulis exponentialibus replicatis

(On unravelling exponential formulas)


The problem Euler addresses in this paper was posed by Condorcet. Euler takes r positive, and α real, then asks for what values the sequence rrαrrαrrrα, ...   converges. The critical value seems to be at r = e1/e = 1.44467.

According to the records, it was presented to the St. Petersburg Academy on June 12, 1777.

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