# coefficient

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Related to Leading coefficient: polynomial, degree of a polynomial

## coefficient

1. Maths
a. a numerical or constant factor in an algebraic term
b. the product of all the factors of a term excluding one or more specified variables
2. Physics a value that relates one physical quantity to another
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Coefficient

a numerical factor in a literal expression, a known multiplier of an unknown quantity of any degree, or a constant multiplier of a variable quantity. Thus, in the monomial −¾ a2b3 the coefficient is −¾; in the equation x2 + 2px + q = 0 the coefficient of x2 is 1 and the coefficient of x is 2p; and in the formula for the circumference of a circle l = 2πr the coefficient is 2π. In the equation for a straight line y = kx + b, the number k, which expresses the tangent of the angle that the line makes with the Ox axis, is known as the slope. Many of the coefficients in formulas expressing physical laws have special names, for example, the coefficient of friction and the coefficient of light absorption.

## coefficient

[¦kō·ə′fish·ənt]
(mathematics)
A factor in a product.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The set of i/o difference equations (1) is called strongly row-reduced if the leading coefficient matrix [L.sub.[mu]] has full rank over [A.sub.l].
Dividing equation (2.20) by the leading coefficient, we have
It remains to examine the leading coefficient, where it turns out that only the summand k = m gives a contribution, and by using equation (17b) we get
1 Compute n zeros, [mathematical expression not reproducible] of pn = [p.sub.n] (*; [[mu].sup.(a,[rho ] )]), and leading coefficient [[gamma]n] of pn.
Rules for Leading Coefficients of the Polynomials [p.sub.[alpha]](k).
In this case, [A.sub.[GAMMA]]([alpha], 1) is a polynomial in g of degree [alpha] - 1 and leading coefficient [2.sup.[alpha]-1][G.sup.[alpha].sub.[alpha]-1]/[alpha]!
We begin with a known transformation that homogenizes the leading coefficient a2(x), and show how it can be used to generalize the stability results from the previous sections.
Summarizing, we see that the Laurent coefficients of S (or of 1/S) contain surprisingly good approximations of two main parameters of the OPUC: they match asymptotically the Verblunsky coefficients, and the partial sums of the squares of their absolute values represent (up to a normalizing constant) the leading coefficient of the orthonormal polynomials.
Condition numbers are found from the Lagrange's representation of the polynomial p(z) where we assume that the leading coefficient [a.sub.n] is known exactly whereas the computed values fl(p([w.sub.i])) satisfy fl(p([w.sub.i])) = p([w.sub.i])(1 + [[epsilon].sub.i]), where [absolute value of [[epsilon].sub.i]] [less than or equal to] n x eps and eps is the machine precision.
Furthermore, taking into account the polar decomposition for the leading coefficient of ([[PHI].sub.n]), we can assume that such a matrix coefficient is a positive definite matrix, and thus, we can choose this normalization in order to have uniqueness for our sequence of matrix orthonormal polynomials [1, page 333].
The other topic is that of descriptor systems, where the leading coefficient of the polynomial is singular.
As shown in [1, 10], we remark that the dominant asymptotic behavior of [[z.sup.n]][W.sub.l](z) and [[z.sub.n]] E]r(z) (for any power series A(z) = [summation] [a.sub.n] [z.sup.n], A(z) denotes the nth coefficient of A(z), namely, [[z.sup.n]]A(z) = [a.sub.n].) is governed by the leading coefficients [b.sub.l] and [e.sub.r].

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