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seen Oct 28 '12 at 11:12

May
18
awarded  Notable Question
Oct
28
accepted How do I compute $\int_{-\infty}^\infty e^{-\frac{x^2}{2t}} e^{-ikx} \, \mathrm dx$ for $t \in \mathbb{R}_{>0}$ and $k \in \mathbb{R}$?
Oct
27
comment How do I compute $\int_{-\infty}^\infty e^{-\frac{x^2}{2t}} e^{-ikx} \, \mathrm dx$ for $t \in \mathbb{R}_{>0}$ and $k \in \mathbb{R}$?
So I found this, thanks for your help I guess...
Oct
27
comment How do I compute $\int_{-\infty}^\infty e^{-\frac{x^2}{2t}} e^{-ikx} \, \mathrm dx$ for $t \in \mathbb{R}_{>0}$ and $k \in \mathbb{R}$?
Could I argue that the integral along this contour vanishes and as the paths left and right (in vertical direction) cancel each other, the integral along the complex path must equal the integral along the real axis and therefore for $T \to \infty$ the integral from $-\infty$ to $\infty$ equals the integral from $-i \infty$ to $i \infty$?
Oct
27
comment How do I compute $\int_{-\infty}^\infty e^{-\frac{x^2}{2t}} e^{-ikx} \, \mathrm dx$ for $t \in \mathbb{R}_{>0}$ and $k \in \mathbb{R}$?
I don't quite understand. Could you maybe tell me what in my case would be $c$? What do I have to use as $f$ in Cauchy's formula?
Oct
27
asked How do I compute $\int_{-\infty}^\infty e^{-\frac{x^2}{2t}} e^{-ikx} \, \mathrm dx$ for $t \in \mathbb{R}_{>0}$ and $k \in \mathbb{R}$?
Oct
23
awarded  Popular Question
Oct
15
awarded  Nice Question
Oct
14
accepted “A proof that algebraic topology can never have a non self-contradictory set of abelian groups” - Dr. Sheldon Cooper
Oct
12
asked “A proof that algebraic topology can never have a non self-contradictory set of abelian groups” - Dr. Sheldon Cooper
Oct
12
awarded  Scholar
Oct
12
accepted Find all homomorphisms $\varphi: C_4 \to V$ or $\psi: V \to C_4$ where $C_4$ is the cyclic group and $V$ the Kleinian group
Oct
11
awarded  Student
Oct
11
asked Find all homomorphisms $\varphi: C_4 \to V$ or $\psi: V \to C_4$ where $C_4$ is the cyclic group and $V$ the Kleinian group