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.
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 5, 1784, pp. 74-111
Opera Omnia: Series 1, Volume 15, pp. 528 - 568
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original Publication: E575
- English draft translation (Alexander Aycock): E575
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