All Questions
5
questions with no upvoted or accepted answers
4
votes
0
answers
306
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Closed form for Sum of Tangents with Angles in Arithmetic Progression
The formulae that can be used to evaluate series of sines and cosines of angles in arithmetic progressions are well known:
$$\sum_{k=0}^{n-1}\cos (a+k d) =\frac{\sin( \frac{nd}{2})}{\sin ( \frac{d}{2} ...
- 6,560
4
votes
1
answer
418
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Write $\sum_{k=1}^nk\sin(kx)^2$ in closed form
$\underline{Given:}$
Write in closed form $$\sum_{k=1}^nk\sin(kx)^2$$
using the fact that $$\sum_{k=1}^nku^k=\frac u{(1-u)^2}[(n)u^{n+1}(n+1)u^n+1]$$
$\underline{My\ Work:}$
I substituted $\sin(kx)^...
- 1,250
3
votes
0
answers
64
views
Signed sum of sin and cos
In the study of graphical representations of the Ising model I have encountered the following sum for natural numbers $a,b$ such that $b \leq a$
$$
\sum_{\theta \in \{ \frac{ 2 \pi k}{q}, k = 0, \dots ...
0
votes
0
answers
66
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Finding Closed Form Representation of A Sum of Trigonometric Functions
Is there a closed form representation of the sum $$\sum_{k=1}^x \cos\left(\frac{n\pi}{k}\right)$$ where $n$ and $x$ are integers? If not possible, is there a representation that uses special functions?...
- 788
0
votes
0
answers
48
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Coefficients of a polynomial with roots represented as squares of cosines
Consider a polynomial with roots $\cos^2 \left(\frac{j \pi}{2n + 1}\right), 1 \leq j \leq n$. The coefficients of this polynomial are sums of these numbers taken one at a time, two at a time, three at ...
