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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

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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).

Related Topics:
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.

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

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