Newton binomial

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binomium of Newton

The formula for the expansion of an arbitrary positive integral power of a binomial in a polynomial arranged in powers of one of the terms of the binomial:



are the binomial coefficients. For terms formula (*) takes the form

For an arbitrary exponent , real or even complex, the right-hand side of (*) is, generally speaking, a binomial series.

The gradual mastering of binomial formulas, beginning with the simplest special cases (formulas for the "square" and the "cube of a sum" ) can be traced back to the 11th century. I. Newton's contribution, strictly speaking, lies in the discovery of the binomial series.


The coefficients

are called multinomial coefficients.

How to Cite This Entry:
Newton binomial. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098