De evolutione potestatis polynomialis cuiuscunque (1 + x + x² + x³ + x⁴ + etc.)ⁿ

English Title

On the expansion of the power of any polynomial (1 + x + x² + x³ + x⁴ + etc.)ⁿ

Authors

Leonhard Euler

Enestrom Number

709

Fuss Index

168

Original Language

Latin

Content Summary

In this paper, Euler gives: (1) the general trinomial coefficient as a sum of binomial coefficients, (2) the general quadrinomial coefficient as a sum of binomial and trinomial coefficients (3) the general quintonomial coefficient as a sum of binomial and quadrinomial coefficients; and (4) a way to determine the coefficients in any polynomial (1+x+x² + ... + x^m)ⁿ as a sum of the coefficients of lower-degree polynomials. (Based on Jordan Bell's translation abstract.)

Published as

Journal article

Published Date

1801

Written Date

1778

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 12, pp. 47-57.

Opera Omnia Citation

Series 1, Volume 16B, pp.28-40.

Record Created

2018-09-25