# 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: (*)  where 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.

#### Comments

The coefficients are called multinomial coefficients.

How to Cite This Entry:
Newton binomial. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Newton_binomial&oldid=13002
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098