### Questions (27)

 8 Does $\sum_{k=0}^{\infty}\sin\left(\frac{\pi x}{2^k}\right)$ have a simple form with interesting properties? 6 Identify $\sum\limits_{k=-\infty}^{\infty} \frac{1}{(x+k)^2}$ 4 Feynman integration - help with this old answer 3 $e^{-xy} + e^{xy} = 2e^{-y}$ - where am I going wrong? 3 What is $\sum_{k=-\infty}^{\infty} \frac{(-1)^k}{x+(2k+1)}$?

### Reputation (592)

 +30 $e^{-xy} + e^{xy} = 2e^{-y}$ - where am I going wrong? +8 Inverse Laplace Transform of dirac-delta $\mathcal{L^{-1}} \delta(x)$ +20 $\int_{0}^{\infty} f(x) \sin(x) dx$ from Complex Fourier Transform for $f(x)$ even +10 $L_{s} [t f(t) f'(t)]$

 1 Convolution periodicity 0 Integrating $\frac {sgn(x)} {x^3}$ 0 Two right triangles of equal perimeter share a side. Given an acute angle of one triangle, find the acute angles of the other. 0 Some servants always tell the truth whereas other servants always lie 0 Help with total probability of a transmitted message (Total probability?)

### Tags (30)

 1 convolution × 2 0 fourier-transform × 4 1 periodic-functions 0 definite-integrals × 3 1 signal-processing 0 functions × 2 0 sequences-and-series × 9 0 summation × 2 0 integration × 6 0 trigonometric-series × 2