# coefficients

1. ### Find Fourier coefficients of g(x) = f(2x)

Hi, I have the following problem: Assume that the function is -periodic and has the Fourier series: Find the Fourier coefficients of the function g(x) = f(2x) As far as I understood, the Fourier coefficients of this function can not be a number, because we don't have the function...
2. ### Interval of Convergence for differing odd/even coefficients of power series

Hello, I am studying for a midterm this week. One of the practice problems is to find the radius of convergence of \sum_{n=0}^{\infty} a_n x^n where a_n = 5^n if n is odd and a_n = 1/3^n if n is even. It took me a while to hazard a guess that I take the smaller of the two radii? Then a =...
3. ### Exponents as Coefficients

Can an exponent ever be considered the coefficient of a variable? For instance, in the expression x^2, what is the coefficient of x? Is it 2, or is it x, since x^2 = x*x?
4. ### Table of coefficients in R

Using R ive made 7 regression models i want to know exactly how this answered (b) A table with the coefficients of the 7possible multiple linear regression models (3 with one input variable, 3 with 2 inputs, and 1 with 3 inputs). I have attatched an image with what i assume is table of...
5. ### Sum of binomial coefficients multiplied by k^2

Evaluate $\displaystyle\sum\limits_{k=1}^{12} {12\choose{k}}k^2$ The answer is 159744.
6. ### Determinant with binomial coefficients.

So i have to find the values of this determinant: but i don't have any good ideas since these coefficients confuse me. I could expand it using first two columns but it doesn't seem easier after that.
7. ### homogeneous differential equation with constant coefficients

Hi, I need some help solving this homogeneous differential equation with constant coefficients for initial condition; y''''-4y=0 and y(0)=1 y(1)=0 y(-1)=0 y(inf)=0 Well I get as far as y=C1*e^(x*sqrt(2)) + C2*e^(-x*sqrt(2)) + C3*cos(x*sqrt(2)) + C4*sin(x*sqrt(2)), but I don't know how to...
8. ### Deriving variable weight from coefficients

Lets say you have a number of variables with different coefficients. say: var1 0.8091 var2 -0.0123 var3 0.1413 var4 0.1367 var5 -0.0506 etc I can see that var1 is responsible for most of the variation within the model, but how do I calculate it's relaive weight compared to the other...
9. ### Solving the DE using undetermined coefficients.

Hello, I have the DE: y'' + 2y'+y=2x \cdot sin(x) and I proceed to solve using the method of undetermined coefficients and some work I got the following equation and I am not sure how to solve for the coefficients: [ \, \alpha \, (2mx+2b+1) \, + \, 2\beta \,] \, cos(x) + [\, \beta \, (-2mx-b-1)...
10. ### Looking for a proof related to one of the characteristic polynomial coefficients

Hi. Given the characteristic polynomial P_A(\lambda)=\sum_{k=0}^{n}a_k\lambda^k of a matrix A\in \mathbb{R}^{n\times n}, it is easy to see why |A|=a_0 (A's determinant is the zero'th coefficient),but why is a_{n-1} in particular is A's trace? that's just plain weird. I looked online for a proof...
11. ### Use the method of undetermined coefficients to solve the given system

This is the system of equations: dx/dt = 2x+3y-16 dy/dt = -x-2y+11 Ok, thus far I have attempted to convert into a matrix which i wasn't sure if i did right: X= (2 3) + (-16) (-1 2) (11) Have i converted this correctly? After this point do i determine the elegenvalues for...
12. ### Binomial Coefficients

I've got a few binomial coefficient questions that I'm not understanding how to work out. The question asks to find the values of the following binomial coefficients (they are in matrix form) - (a) (11) (3) (b) (9) (7) (c) (100) (99) Help is much appreciated, thanks!
13. ### how to interpret coefficients in Mediation Analysis with logged variables

Hello there! I really hope u can help me because i've tried to find a solution to my problem for ages now.. i'm performing a mediation analysis with two regressions to get the coefficients a b and c. i know the interpretation of indirect effect (a*b) in mediation analysis when there is no...
14. ### Partial Fraction Coefficients

What is the best strategy for finding coefficients, given the following scenarios: A. Distinct linear factors. Ex: (x + 3) (x + 2) etc.. Equation System, or Substitution method B. Repeated Linear Factors Ex (x + 3)^{2} or x^{2} ? C. Irreducible Quadratic (x^{2} + 25) Equation System...
15. ### Finding several values of unknown coefficients

I have no problem finding at least one kind of unknown coefficient but there are several 2(ax+1)+b=6x-2 This is what I've tried Expanding the brackets first 2ax+2+b=6x-2 Then I moved the two from the left, to the right 2ax+b=6x-4 I wondered whether I could divide 6x by 2x without the a...
16. ### If (x - a)(x - b)^3 has integer coefficients, then a, b are integers

Show taht if polynomial $(x -a) (x-b)^3$ has integer coefficients, then $a,b$ are integers.
17. ### All binomial coefficients (n p) are divisible by a prime p only if n is a power of p

I'm looking for a "high school / undergraduate" demonstration for the: All the binomial coefficients $\binom{n}{i}$ where $0\lt i \lt n$, are divisible by a prime p only if n is a power of p. There is a "elementary" demonstration of reciprocal here...
18. ### Restraining quadratic equation to positive coefficients

Hi, I am a postgraduate student carrying out air quality research for my thesis. I have determined a best fit quadratic equation with a zero intercept (y = 1.1133x2 – 0.0844x) using OLS regression analysis (MS Excel 2013) for a small dataset. As you can see, this has resulted in a negative...
19. ### finding coefficients

determine a,b and c such that formula _ / h | f(x) dx = h(af(0) + bf(h / 3) + cf(h)) _/ 0 is exact for polynomial of as high order as possible.Also determine the...
20. ### Fourier coefficients of real functions are real

Hello. I am asked to show that fourier coefficients of a function that just takes real values a_n,b_n are real. It seems pretty obvious but I can't find a proof, Any help? Thank you very much!!