New posts in trigonometric-series

Limit of maximum of $f_{n}(x)=\frac{1}{n}(\sin{x}+\sin{(2x)}+\cdots+\sin{(nx)})$

real-analysis sequences-and-series limits fourier-analysis trigonometric-series

Does $\sum_{k=0}^{\infty}\sin\left(\frac{\pi x}{2^k}\right)$ have a simple form with interesting properties?

sequences-and-series summation trigonometric-series

Find the Maximum Trigonometric polynomial coefficient $A_{k}$

algebra-precalculus trigonometry inequality trigonometric-series

Evaluation of $ \sum_{k=0}^n \cos k\theta $

trigonometry summation trigonometric-series

Study the sequence $x_n=\sqrt[n]{2^{n\sin 1}+2^{n\sin 2}+\cdots+2^{n\sin n}}$.

calculus sequences-and-series limits convergence-divergence trigonometric-series

Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

calculus real-analysis sequences-and-series convergence-divergence trigonometric-series

How to prove $\sum_{k=1}^n \cos(\frac{2 \pi k}{n}) = 0$ for any n>1? [duplicate]

sequences-and-series complex-analysis trigonometry complex-numbers trigonometric-series

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

sequences-and-series trigonometry power-series trigonometric-series

Calculate: $\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$

sequences-and-series trigonometry trigonometric-series

Taylor series expansion for $\cos(2x)$ about $\frac{\pi}{8}$

sequences-and-series derivatives taylor-expansion trigonometric-series

Prove $\sum_{k=1}^m \cot^2 k\pi/(2m+1)=m(2m-1)/3$

real-analysis calculus trigonometric-series

Example of a trigonometric series that is not fourier series?

calculus trigonometry fourier-series trigonometric-series

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$

calculus real-analysis sequences-and-series closed-form trigonometric-series

Prove or disprove that $ \sum\limits_{k = 1 }^T f(k)=0 $ where $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin(\frac{n(n+1)(2n+1)}{6}x) $

sequences-and-series trigonometric-series

What is known about sums of the form $\sum_{n=-\infty}^{\infty} \operatorname{sinc} (n^{p})$?

sequences-and-series reference-request definite-integrals trigonometric-integrals trigonometric-series

Need help with calculating this sum: $\sum_{n=0}^\infty\frac{1}{2^n}\tan\frac{1}{2^n}$

calculus sequences-and-series trigonometry closed-form trigonometric-series

Extensions of Ramanujan's Cos/Cosh Identity

sequences-and-series number-theory trigonometry trigonometric-series

Why does a fourier series have a 1/2 in front of the a_0 coefficient

analysis trigonometry fourier-analysis fourier-series trigonometric-series

Does $\sum\limits_{x=1}^\infty\sin(x)$ converge?

sequences-and-series convergence-divergence trigonometric-series

What is the sum over a shifted sinc function?

summation fourier-series signal-processing trigonometric-series