On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc
Abstract
Description
In this paper, Euler gives the general trionomial coefficient as a sum of the binomial coefficients, the general quadrinomial coefficient as a sum of the binomial and trinomial coefficients, the general quintonomial coefficient as a sum of the binomial and quadrinomial coefficients, and gives a general determination of the coefficients of the expansion of any polynomial (1+x+x^2+...+x^m)^n as a sum of the coefficients of lower degree polynomial coefficients.
8 pages. Seems to be first English translation of Euler's Latin original ``De evolutione potestatis polynomialis cuiuscunque (1+x+x^2+x^3+x^4+etc.)^n, Nova Acta Academiae Scientarum Imperialis Petropolitinae 12 (1801), 47-57
8 pages. Seems to be first English translation of Euler's Latin original ``De evolutione potestatis polynomialis cuiuscunque (1+x+x^2+x^3+x^4+etc.)^n, Nova Acta Academiae Scientarum Imperialis Petropolitinae 12 (1801), 47-57