Prove that $\sum _{n=-\infty }^{\infty } e^{-n^2 \pi x}=\frac{1}{\sqrt{x}}\sum _{n=-\infty }^{\infty } e^{-\frac{n^2 \pi }{x}}$
26113
Proving the functional equation $\theta (x) = x^{-\frac{1}{2}} \theta (x^{-1})$ from the Poisson summation formula
124615
Proving convergence of sums: If $\sum_{n=1}^{\infty}a^2_n$ and $\sum_{n=1}^{\infty}b^2_n$ converge then $\sum_{n=1}^{\infty}a_nb_n$ converges
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
124002
How prove this series $\sum_{n=1}^{\infty}\frac{e^n\cdot n!}{n^n}$ divergent
62417
Prove This Inequality ${\pi \over 2} \le \sum_{n=0}^{\infty} {1 \over {1+n^2}} \le {\pi \over 2} + 1$
137249
find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
72748
Proof that $\sum\limits^{\infty}_{i=0}{iP(X > i)} = \frac12(E(X²)-E(X))$ for $X$ nonnegative and integer valued
94943
Sum of series with addition: $\sum_{n=1}^\infty \frac{1}{n^2(n+1)}$
24558
Show that $\frac{1}{\sqrt{2\pi}} \cdot \left(\int_{- \infty}^{\infty} e^{itx} \cdot e^{-\frac{1}{2}t^2 } dx \right) = e^{-\frac{1}{2}t^2}$
93690
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
137640
Proof that $\sum_{1}^{\infty} \frac{1}{n^2} <2$
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
132126
Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
45440
$\sum_{n=2}^\infty \frac{1}{(\ln\, n)^2}$ c0nvergence