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

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dc.creatorEuler, Leonhard
dc.date2005-05-20
dc.date.accessioned2026-07-07T05:20:05Z
dc.date.available2026-07-07T05:20:05Z
dc.descriptionIn 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.
dc.description8 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
dc.identifierhttps://arxiv.org/abs/math/0505425
dc.identifierhttp://arxiv.org/abs/math/0505425
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75251
dc.subjectHistory and Overview
dc.subjectCombinatorics
dc.subject01A50; 05A10
dc.titleOn the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc
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