Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression. For instance in

the first three terms respectively have the coefficients 7, −3, and 1.5 (in the third term the variables are hidden (raised to the 0 power), so the coefficient is the term itself; it is called the constant term or constant coefficient of this expression). The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c in

when it is understood that these are not considered as variables. Thus a polynomial in one variable x can be written as

for some integer, where are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient. For the largest with (if any), is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial

is 4.

Specific coefficients arise in mathematical identities, such as the binomial theorem which involves binomial coefficients; these particular coefficients are tabulated in Pascal's triangle.