# What is Coefficients: Definition and 803 Discussions

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c). When variables appear in the coefficients, they are often called parameters, and must be clearly distinguished from those representing other variables in an expression.
For example,

2

x

2

x
+
3

{\displaystyle 2x^{2}-x+3}
, has the real coefficients 2, -1, and 3 respectively, and

a

x

2

+
b
x
+
c

{\displaystyle ax^{2}+bx+c}
, has coefficient parameters a, b, and c respectively assuming x is the variable of the equation.
The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the real coefficient 3 and the parameter represented by c.
Similarly, the coefficient attached to the highest multiplicity of the variable in a polynomial is referred to as the leading coefficient. For example in the expressions above, the leading coefficients are 2 and the parameter represented by a.
The binomial coefficients occur in the expanded form of

(
x
+
y

)

n

{\displaystyle (x+y)^{n}}
, and are tabulated in Pascal's triangle.

View More On Wikipedia.org

2. ### A Margules' Power Series Formula: Deriving Coefficients

Margules suggested a power series formula for expressing the activity composition variation of a binary system. lnγ1=α1x2+(1/2)α2x2^2+(1/3)α3x2^3+... lnγ2=β1x1+(1/2)β2x1^2+(1/3)β3x1^3+... Applying the Gibbs-Duhem equation with ignoring coefficients αi's and βi's higher than i=3, we can obtain...
3. ### A The standardized and unstandardized canonical correlation coefficients

The output of SPSS 27 Canonical Correlation gives the standardized and unstandardized canonical correlation coefficients. What exactly are the standardized and unstandardized canonical correlation coefficients and what is the difference between them?
4. ### How to Approximate Aerodynamic Coefficients? (Lift/Drag)

Hello, this is a very specific question so any help is much appreciated! GOAL: I'm trying to get a first-pass analytical approximation for the lift and drag coefficients for hypersonic flow over a blunt-body capsule spacecraft (similar to NASA's Apollo or SpaceX's Dragon) during atmospheric...
5. ### I Linear regression, feature scaling, and regression coefficients

Hello, In studying linear regression more deeply, I learned that scaling play an important role in multiple ways: a) the range of the independent variables ##X## affects the values of the regression coefficients. For example, a predictor variable ##X## with a large range typically get assigned...
6. ### Engineering How to implement a transfer function in Simulink with variable coefficients?

The implementations for the two filters in simulink are as follow: For the first filter: For the second one: The obtained results have values of 10^-12, while the expected results should be between 10^-3 - 10. Since it's the first time when I try t implement a tf with variable coefficients I...
7. ### A Expression of Shot noise when expanding ##a_{\ell m}## coefficients

I would like to arrive at the following expression for the quantity ##o_{\ell}## ( with "DM" for Dark Matter ): ##o_{\ell}=b_{s p}^2 C_{\ell}^{D M}+B_{s p}## with Poisson noise ##B_{s p}=\frac{1}{\bar{n}}(\bar{n}## being the average number of galaxies observed). the index "sp" is for spectro...
8. ### Comp Sci Plot periodic function with Fourier coefficients

I have plotted the function for ##T=15## and ##\tau=T/30## below with the following code in Python: import numpy as np import matplotlib.pyplot as plt def p(t,T,tau): n=np.floor(t/T) t=t-n*T if t<(2*np.pi*tau): p=np.sin(t/tau) else: p=0 return p...
9. ### How do I find the coefficients of static friction and kinetic friction?

I have found that μstatic= 5.6 (found on graph) / 18.20 = 0.3077 I don't know how to find Force of friction from the graph to calculate μKinetic
10. ### Characterize Fourier coefficients

I would try to determine whether ##p(t)## is even or odd. This would be so much easier if the values of ##\tau## and ##T## would be specified, but maybe it's possible to do without it, which I'd prefer. If for example ##\tau=1/2## and ##T=2\pi##, then ##p(t)=\sin{(2t)}## for ##0\leq t <\pi ##...
11. ### I Second Order ODE with Exponential Coefficients

Hi all, I have another second order ODE that I need help with simplifying/solving: ##p''(x) - D\frac{e^{\gamma x}}{A-Ae^{\gamma x}}p'(x) - Fp(x) = 0## where ##\gamma,A,F## can all be assumed to be nonzero real numbers and ##D## is a purely nonzero imaginary number. Any help would be appreciated!
12. ### Friction Coefficients: Determining Force Direction?

Do I determine this from the friction coefficients? Such that because mu_b > mu_a I know that it'll push on B because it has a bigger friction coefficient. such that this has nothing to do with the mass of the blocks? or does it? f.e. can I take it to be in an arbitrary direction and then...
13. ### B Dividing Lamé coefficients

Sometimes in calculations authors uses \frac{1}{h_1h_2}=\frac{h_3}{h_1h_2h_3} where ##h_i, i=1,2,3## are Lame coefficients. For instance in spherical coordinates ##h_r=1##, ##h_{\theta}=r##, ##h_{\varphi}=r\sin \theta##. I am not sure how we can divide so easily Lame coefficients when some on...
14. ### I Transformation of connection coefficients

I don't understand why the highlighted term is there. This image was taken from Sean Carroll's notes available here: preposterousuniverse.com/wp-content/uploads/grnotes-three.pdf
15. ### Method of detached coefficients division

-1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5 1 2 -3 7 9 -31 15 7 14 -21 -5 -10 15 5 -10 15The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be...
16. ### Finding specific heat C_p coefficients using NIST

I am trying to find the specific heat (at constant pressure) ##C_p## coefficients linked to the JANAF model, which basically assumes that ##C_p## is a polynomic function of ##T##, for liquid nitrogen (at ##\approx## 97 K). Before doing that, I am trying to find those for water (at ##\approx##...

26. ### Find the Fourier Coefficients

Consider the function ##f:[0,1]\rightarrow \mathbb{R}## given by $$f(x)=x^2$$ (1) The Fourier coefficients of ##f## are given by $$\hat{f}(0)=\int^1_0x^2dx=\Big[\frac{x^3}{3}\Big]^1_0=\frac{1}{3}$$ $$\hat{f}(k)=\int^1_0x^2e^{-2\pi i k x}dx$$ Can this second integral be evaluated?
27. ### Scientific Computing: Method of Undetermined Coefficients in Python

In a self learning project I am fooling around book https://faculty.washington.edu/rjl/fdmbook/ I want to do some of the computation myself to better understand the concepts but the book is Matlab based and Matlab is too expensive. Does anyone by any chance have some of the codes provided by...
28. ### If a polynomial is identically zero, then all its coefficients are 0

Suppose ##a_0+a_1x+\ldots+a_nx^n=0## and restrict the domain of ##p## to the set of real numbers excluding the roots of ##p##. Note that: if ##a_0 == 0##: ##x=0## is a root of ##p## else: ##x=0## is not a root of ##p## Assume the latter. Subtract ##a_0## from both sides of the equation...
29. ### Coefficients in the expansion of (1+x)n in A.P, find n

https://www.toppr.com/ask/question/if-in-the-expansion-of-1-xn-the-coefficient-of-14th-15th-and-16th/ https://www.sarthaks.com/402983/if-in-the-expansion-of-1-x-n-the-coefficients-of-14-th-15-th-and-16-th-terms-are-in-a-p-find-n Specifically regarding my problem the coefficients of x^8, x^9 and...

45. ### Engineering Fourier series coefficients

i tired using complex identity equation for sin(pi*k/3) but it doesn't work out
46. ### I How can a photon "stimulate emission" if it really does (Einstein coefficients)

Einstein coefficients tell us that there is some probability for an atom to go from E_1 to E_2 given by the coefficient of absorption. This is fine, but why is there only one coefficient (absorption) going from E_1 to E_2 and two for the transition E_2 to E_1? Spontaneous emission makes sense...
47. ### Lift and drag coefficients vs AoA graphs of a specific NACA profile

Hello, I would like to understand know how the lift coefficient ##C_L## versus AoA curve and the drag coefficient ##C_D## versus AoA curve are determined for the various tabulated NACA profiles. Are computer simulation run for the different profiles assuming a certain Reynolds' number? Or can...
48. ### Engineering Reconstruct a signal by determining the N Fourier Coefficients

%My code: %Type of signal: square T = 40; %Period of the signal [s] F=1/T; % fr D = 23; % length of signal(duration) dt=(D/T)*100; N = 50; %Number of coefficientsw0 = 2*pi/T; %signal pulset1= 0:0.002:T; % original signal sampling x1 = square((2*pi*F)*(t1),dt);%initial square signal t2=...
49. ### I Separation of variables - Getting the Fourier coefficients

Hey there! I am current taking an introductory course on PDE's, and our professor hasn't really emphasized last part of solutions from separation of variables. Now its not strictly going to be on the exam, however I remember doing this with ease a few years back, but for some reason now I...
50. ### Engineering Sectional Lift/Moment coefficients w/ sinusoidal motion

I cannot figure out how to even start this.