On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc

Details On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc

2005-05-20

arxiv.org/abs/math/0505425v1

Mathematics

History and Overview

8 pages. Seems to be first English translation of Euler's Latin original ``De evolutione potestatis polynomialis cuiuscunque

Scientific paper

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.

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