E575 -- De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt

(English Translation of Title)


First, Euler gives a few relations on products and sums of binomial coefficients, then a relation on the sums of squares of binomial coefficients. Then he does a bit with the integral for the beta function and finds analogous relations for sums and products of generalized binomial coefficients.

This article is notable also in part because Euler uses a fairly modern looking notation for binomial coefficients. Specifically, he writes [m/n].

According to the records, it was presented to the St. Petersburg Academy on May 13, 1776.

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