Coefficient

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For other senses of this word, see coefficient (disambiguation).

In mathematics, a coefficient is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient of 9x² is 9. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as

[a_1 x_1 + a_2 x_2 + a_3 x_3 + \cdots ]

where a_n is the coefficient of the variable x_n for each n = 1, 2, 3, …

In a polynomial P(x) of one variable x, the coefficient of x^k can be indexed by k, giving the convention that for example

[P(x) = a_k x^k + \cdots + a_1 x^1 + a_0]

For the largest k where a_k ≠ 0, a_k is called the leading coefficient of P because most often, polynomials are written from the largest power of x, downward (i.e. x⁵ + x⁴ + x² ...).

Important coefficients in mathematics include the binomial coefficients, coefficients in the statement of the binomial theorem, which can be partially found with Pascal's triangle.

Coefficient

See also