E465 -- Demonstratio theorematis Neutoniani de evolutione potestatum binomii pro casibus, quibus exponentes non sunt numeri integri

(A demonstration of a theorem of Newton on the expansion of the powers of a binomial by cases, in which the exponents are not integral numbers)


In Calculus Differentialis, Euler showed that (1 + x)a = 1 + C(a, 1)x + C(a, 2)x2 + .... . Here, Euler shows it to be true for arbitrary real values of a and makes use of the functional equation that if f(a) = (1 + x)a, then f(a)f(b) = f(a + b).

According to the records, it was presented to the St. Petersburg Academy on July 1, 1773.

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