In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number...

The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident...

the Dedekind eta function. Expanding into series of powers and equating coefficients of θ0, θ4, and θ8 gives some deep identities for the hyperbolic...

F(x)=F_{1}x+F_{2}x^{2}+F_{3}x^{3}+\cdots ={\frac {x}{1-x-x^{2}}},} and equating coefficients on both sides of F ( x ) ( 1 − x − x 2 ) = x {\displaystyle F(x)(1-x-x^{2})=x}...

useful heating or cooling provided to work (energy) required. Higher COPs equate to higher efficiency, lower energy (power) consumption and thus lower operating...

relation for infinitesimal rotations and the Baker Hausdorff lemma, by equating coefficients of order δ θ {\displaystyle \delta \theta } , one can derive the...

above. As a correlation coefficient, the Matthews correlation coefficient is the geometric mean of the regression coefficients of the problem and its dual...

always separate, we regroup the terms, x2 − y2 + 2ixy = 0 + i. By equating coefficients, separating the real part and imaginary part, we have a system of...

\&=x^{4}+(s+u)x^{3}+(t+v+su)x^{2}+(sv+tu)x+tv\end{aligned}}} By equating coefficients, this results in the following system of equations: { b = s + u...

|}_{Q,P,t}} which is independent of dynamics of the particles, equating coefficients of q ˙ {\textstyle {\dot {q}}} and p ˙ {\textstyle {\dot {p}}} to...

}}\int (c-c_{0})\exp(-i\beta x)~dx} Substituting, we obtain on equating coefficients: d A ( β ) d t = − M N ν [ f ″ + 2 η 2 Y + 2 Y β 2 ] β 2 A ( β )...

\&=x^{4}+(p+r)x^{3}+(q+s+pr)x^{2}+(ps+qr)x+qs\end{aligned}}} By equating coefficients, this results in the following set of simultaneous equations: b...

ISBN 978-3-319-73220-6. Hersey, equation (2), p. 83 Астахов, p. 81. "Coefficients of Friction in Bearing". Coefficients of Friction. Retrieved 7 February 2012. ETH - PAC-Car...

several reliability coefficients. The majority opinion is to use structural equation modeling or SEM-based reliability coefficients as an alternative to...

linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solutions of such an...

}{\partial y}}dy.} Substituting dy into the latter differential and equating coefficients of the differentials gives the first order partial derivatives of...

_{n=0}^{\infty }a_{n}x^{n}\right)=1.} Multiplying out the left hand side and equating coefficients on the two sides, we obtain a0 p(0) = 1 and ∑ i = 0 n p ( n − i...

explicit. Extraneous and missing solutions Simultaneous equations Equating coefficients Solving the geodesic equations Unification (computer science) —...

After expanding the representation multiplication equation and equating coefficients, we have the nontrivial condition t b c = − t b t c − i ∑ a f a...

algorithm computes these coefficients more efficiently [clarification needed]. When the characteristic of the field of the coefficients is 0 , {\displaystyle...

terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not...

linear algebra, and dynamical systems), a linear recurrence with constant coefficients: ch. 17 : ch. 10  (also known as a linear recurrence relation or linear...

are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the...

substitution, by equating the coefficients of terms involving the powers of x, or otherwise. (This is a variant of the method of undetermined coefficients. After...

be supposed to have integer coefficients, and leading and constant coefficients dividing the corresponding coefficients of P. In the polynomial 2 x 3...

{n}})^{k},} expanding the right side, equating coefficients of n {\displaystyle {\sqrt {n}}} on both sides, and equating the other terms on both sides. This...

{\displaystyle a} ⁠, ⁠ b {\displaystyle b} ⁠, and ⁠ c {\displaystyle c} ⁠ are coefficients. The expression ⁠ a x 2 + b x + c {\displaystyle \textstyle ax^{2}+bx+c}...

+c_{m+n}z^{m+n}\right)=P_{m}(z)} and equating coefficients of like powers of z up through m + n. For the coefficients of powers m + 1 to m + n, the right...

polynomial), expanding the products in the right-hand side, and equating the coefficients of each power of x {\displaystyle x} between the two members of...

polynomial does not introduce divisions of coefficients. Therefore, it is defined for polynomials with coefficients in a commutative ring. Algebraic integers...