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

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: a1x1 + a2x2 + a3x3 + …

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

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

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

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Here if

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:an ≠ 0

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

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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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Multiplicative: Multiplicative may refer to:...

Variable: In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. In mathematics, a variable often represents an unknown quantity; in computer science, it represents a place where a quantity can be stored. Variables are often contrasted with constants, which...

Polynomial: In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. Here, simple means they are constructed using only multiplication and addition. Smooth means they are infinitely differentiable, i.e., they have derivatives of all finite orders....