Coefficient Definition and 1000 Threads

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.

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  1. 5P@N

    Need help understanding a lift coefficient formula

    Please go to this Wikipedia article on Lift Coefficients, and behold the first formula. The last part of the equation has a "S" which is supposed to stand for "relevant plan area". Now, there was no explanation of what this "relevant plan area" is or means. I was guessing that it means the...
  2. D

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  3. Capisko

    What is the definition of the coefficient of linear and mass

    hi, i'm student in a university. I do not understand the definition of these concepts, and I would like to know the properties of these and it depends questions like They depend on the material used? the atomic number? thanks for answering capisko,
  4. M

    Heat Transfer Coefficient -Air Flow onto perpendicular plane

    Hi All, I have a situation were I need to evaluate the heat transfer coefficient of a horizontal surface. The surface has tubes within although I first used "flow across a bank of tubes", this has been untrue due to the air flow coming from above the surface flowing vertically (and...
  5. R

    Proving Spin Coefficient Transformation for Null Rotation with l Fixed

    In Newmann-Penrose formalism, a Null rotation with ##l## fixed is $$l^a−>l^a\\ n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\ m^a−>m^a+cl^a\\ \bar{m}^a−>\bar{m}^a+\bar{c}l^a$$ Using this transformation, how to prove? $$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$ Ref: 2-Spinors by P.O'Donell, p.no, 65
  6. ognik

    MHB Fourier series coefficient problem

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  7. S

    Concentration of C6Cl6 in a sediment core w/ diffusion coefficient

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  8. E

    Why does the mass attenuation coefficient have a negative gradient?

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  9. T

    What is the Coefficient of Friction for a Lab Using Spring Scales?

    Homework Statement I'm having trouble finding the coefficient of kinetic friction for a lab using spring scales. Mass=.411kg Normal Force=4.0278 Average Pull Force=.46N Frictional Force= -.46NHomework Equations μ k = Fk / N. The Attempt at a Solution μ k = -.46N/4.0278 μ k = -.1142
  10. Schwarzschild90

    Partition coefficient of chlorpromazine in DMSO & pentane

    Determine the partition coefficient of chlorpromazine in DMSO and n-pentane I'm a physics student and doing a course in biophysics. I would really appreciate it, if you would take some time and provide some hints as to how to design a more concrete plan. Especialy, how do I find out the...
  11. Rishi Saxena

    Frictional Coefficient for Glass

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  12. M

    What Causes a Negative Drag Coefficient in Projectile Trajectory?

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  13. C

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  14. F

    How to write imaginary coefficient in excel 2013

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  15. Odious Suspect

    Binomial Coefficient Factorial Derivation

    A few decades ago my algebra teacher showed how to construct the expression for binomial coefficients. If I start with Pascal's recursion, and propose C(n,k)=n!/k!(n-k)!, I can prove it to be so through induction. But that doesn't give me that happy feeling that comes with understanding. It...
  16. Mrchilko

    Finding friction w/ out coefficient?

    Homework Statement Hey new to forum here... Grade 11 physics student... Love physics and math! But this one question seems easy but I can't seem to get through... Here it is : A 1100kg car accelerates at 3.40 m/s. If the wheels exert a force of 5600N on the road, calculate the force of friction...
  17. K

    Coefficient of static friction on a ramp?

    Homework Statement A small block sits at the midpoint of a 2.0 m plank lying on a level floor. A student slowly raises one end of the plank until the block starts to slide. At that instant, the raised end is 0.55 m above the floor. Find the coefficient of static friction between block and...
  18. K

    Force tension, friction, and coefficient of friction

    Homework Statement A child pulls a friend on a sled. The child maintains a constant tension of 29.4 N in the rope. The combined mass of the friend and sled is 30.0 kg, and the coefficient of sliding friction between the sled and snow is 0.1. How far can the child pull her friend in 6 sec...
  19. E

    Overall heat transfer coefficient for free convection exchanger

    I am trying to design a heat exchanger for a stratified hot water tank which means that the heat transfer on that side of the exchanger will be totally dependent on free convection. I plan on using a shell and tube set-up but I have no idea on how to calculate the required mass flow rate from...
  20. H

    Coefficient of friction different for different angles.

    I am having my students do a lab to calculate the coefficient of static friction along a ramp. They are calculating the coefficient of static friction between felt and the table to be something like 0.40, yet when i did this lab, but along a horizontal surface, and not with a ramp, i get a...
  21. W

    C_0 coefficient of Complex Fourier transforms

    Mod note: Moved from technical math section, so no template was used. Hey! So the complex Fourier transform of the square wave $$ f(x) = \begin{cases} 2 & x \in [0,2] \\ -1 & x \in [2,3] \\ \end{cases}, \space \space f(x+3) = f(x)$$ is ##C_k = \frac{3j}{2 \pi k}( e^{-j \frac{4 \pi k}{3}}...
  22. ChloeYip

    Reaction Coefficient: 2IO3-+wH2O2+xH+=>I2+yO2+zH2O - Answers Explained

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  23. R

    Coefficient of restitution in different frames of references

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  24. J

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  25. C

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  26. G

    Determine the force involving static coefficient

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  27. W

    Determine static coefficient of friction

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  28. Sace Ver

    Calculate the coefficient of kinetic friction for a sliding box

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  29. M

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  30. L

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  31. B

    Finding friction coefficient, car unbanked curve.

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  32. K

    Finding the coefficient of Kinetic force with an angle

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  33. B

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  34. B

    Coefficient of Kinetic Friction

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  35. L

    Can The Joule Coefficient be Derived Using the First Law and Maxwell Relation?

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  36. K

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  37. S

    Coefficient of friction on an inclined plane?

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  38. Arlan

    Calculating Rebound Height for a Ball Colliding with Steel Plate

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  39. A

    Finding friction force *without* mass or coefficient

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  40. T

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  41. O

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  42. L

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  43. merlyn

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  44. Weightofananvil

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  45. P

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  46. Chrono G. Xay

    Can We Predict Damping Coefficient of a String Using Mathematical Simulation?

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  47. Z

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  48. erickbq

    [Statics - Torques] Determining Coefficient of Static Friction

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  49. duc

    Coefficient of a polynomial defined by Legendre polynomial

    Homework Statement The polynomial of order ##(l-1)## denoted ## W_{l-1}(x) ## is defined by ## W_{l-1}(x) = \sum_{m=1}^{l} \frac{1}{m} P_{m-1}(x) P_{l-m}(x) ## where ## P_m(x) ## is the Legendre polynomial of first kind. In addition, one can also write ## W_{l-1}(x) = \sum_{n=0}^{l-1} a_n \cdot...
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