Coefficient

In mathematics, a coefficient is a 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

Related Topics:
Mathematics - Multiplicative - Variable - Polynomial - Basis vector - Basis function

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: a1x1 + a2x2 + a3x3 + …

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

where an is the coefficient of the variable xn for each n = 1, 2, 3, ?

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:P(x) = anxn + an − 1xn − 1 + ... + a1x1 + a0.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here if

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:an ≠ 0

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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

Related Topics:
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.

Related Topics:
Binomial coefficient - Binomial theorem - Pascal's triangle

~ ~ ~ ~ ~ ~ ~ ~ ~ ~