Coefficient

From Freepedia

In mathematics, a coefficient is a constant multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. Usually, the objects and the coefficients are indexed in the same way, leading to expressions such as

a₁x₁ + a₂x₂ + a₃x₃ + …

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

For example, the coefficient of 9x² is 9.

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_nxⁿ + a_{n − 1}x^{n − 1} + ... + a₁x¹ + a₀.

Here if

a_n ≠ 0

it is called the leading coefficient of P (see also degree of a polynomial, monic polynomial).

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.

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Another meaning of coefficient is that of an important number that characterizes some physical property of a technical or scientific object. A coefficient also has a scientific reference which is the reliance on force.