All Questions
5
questions
7
votes
3
answers
275
views
Proof of a neat pattern in polynomials
Let $f_1:\mathbb{R}\to\mathbb{R}$ such that $$f(x) = ax + b\space\space \forall\space x \in \mathbb{R}$$
It can be easily verified that $$f(x)-2f(x-1)+f(x-2)=0 \space \forall \space x \in
\mathbb{R}--...
- 271
5
votes
1
answer
94
views
Finding coefficient of $j^2k^3lm^3$ in $(j + k + l + m)^9$
I'm trying to find the coefficient of:
$$j^2k^3lm^3$$
in:
$$(j + k + l + m)^9$$
According to the Book of Proof (which is our material), it seems for:
$$x^ay^b, \{a,b\} \in \mathbb{N}$$
in:
$$(x+...
- 160
11
votes
4
answers
12k
views
Finding coefficient of polynomial?
The coefficient of $x^{12}$ in $(x^3 + x^4 + x^5 + x^6 + …)^3$ is_______?
My Try:
Somewhere it explain as:
The expression can be re-written as: $(x^3 (1+ x + x^2 + x^3 + …))^3=x^9(1+(x+x^2+x^3))^3$
...
- 4,785
1
vote
0
answers
17
views
The $k$_th coefficient of the polynomial :$f_n(z)f_m(jz)+f_m(z)f_n(jz) $
Let $j=e^{2i\pi/3}$ ( $i$ is the complex number $i^2=-1$), and let :
$$f_n(z)=(1+z)^n$$
Question Is there an expression (without using sums) of the $k$_th coefficient of the following polynomial :$...
- 13.8k
8
votes
4
answers
49k
views
Get polynomial function from 3 points
I need to understand how to define a polynomial function from 3 given points. Everything I found on the web so far is either too complicated or the reversed way around. (how to get points with a given ...
- 183