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

Published as

Journal article

Published Date

1801

Written Date

1778

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 + ... + xm)n as a sum of the coefficients of lower-degree polynomials. (Based on Jordan Bell's translation abstract.)

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

Included in

Mathematics Commons

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