E637 -- Nova demonstratio, quod evolutio potestatum binomii Newtoniana etiam pro exponentibus fractis valeat

(A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents)


Here Euler notes the recursive relation for the general binomial coefficients, that if (1 + x)a = Sn = 0a n xn and if (a + x)a + 1 = Sn = 0 bn xn, then bn = an + an - 1, generalizing the usual recursive relationship for the binomial coefficients.
Presented to the Academy on May 20, 1776.

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