Random Variable
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 Apr 21 awarded Popular Question Apr 17 revised Examples of adding a constant to integration by parts. added 601 characters in body Apr 14 comment Show that $\int_{C} \frac{e^{az}}{\sin(\pi z)} \,dz \rightarrow 0 \quad as \quad R \rightarrow \infty$ Since $|e^{az}| = e^{\text{Re}(a) \, \text{Re}(z)} e^{- \text{Im}(a) \text{Im}(z)}$ and $\left| \sin (\pi z) \right| \sim \frac{1}{2} e^{\pi \text{Im}(z)}$ as $\text{Im}(z) \to + \infty$, it looks like the integral should vanish if $\text{Im} (a) > -\pi$. Apr 12 revised Showing that $\int_{-\infty}^{\infty} \frac{\sinh ax}{\sinh \pi x} \, \cos bx \, dx = \frac{\sin a}{\cos a + \cosh b}$ deleted 132 characters in body Apr 12 revised Showing that $\int_{-\infty}^{\infty} \frac{\sinh ax}{\sinh \pi x} \, \cos bx \, dx = \frac{\sin a}{\cos a + \cosh b}$ deleted 205 characters in body; edited title Apr 6 revised Closed form for $\sum_{k=1}^\infty(\zeta(4k+1)-1)$ corrected notation Apr 4 accepted Integrating around a pole Apr 2 revised Moving a limit inside an integral deleted 32 characters in body Apr 2 accepted If $\int_{0}^{\infty} f(x) \, dx$ converges, will $\int_{0}^{\infty}e^{-sx} f(x) \, dx$ always converge uniformly on $[0, \infty)$? Mar 31 revised Branch points of the Lambert W function corrected notation Mar 30 awarded Necromancer Mar 30 revised Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$ corrected notation Mar 30 revised Show that $\frac{\Gamma(n+k)}{\Gamma(n)}\sim n^k$ for large values of n deleted 13 characters in body Mar 30 answered Show that $\frac{\Gamma(n+k)}{\Gamma(n)}\sim n^k$ for large values of n Mar 28 revised How do I show that $\int_0^\infty \sin(ax) \sin(bx) / x^2 = \pi \min(a,b)/2$ added 4 characters in body Mar 28 answered How do I show that $\int_0^\infty \sin(ax) \sin(bx) / x^2 = \pi \min(a,b)/2$ Mar 23 revised Deriving Separate Forms of the Error Function I added a tag. Mar 23 comment Deriving Separate Forms of the Error Function You're welcome. Mar 23 revised Deriving Separate Forms of the Error Function added 20 characters in body Mar 23 revised Deriving Separate Forms of the Error Function added 1 character in body