Recent content by Aquinox

Sorry. The way hinted to me in the paper is that we have to take that t^(-1/2) definition and use fubini's thm. This leads to the aforementioned \int_{0}^{\infty}\frac{u^{2}}{1+u^{4}}du I am perfectly able to integrate the RHS of the equation you've posted, but...

That is the answer I, too, have derived from the solutions Mathematica gave me. What I need to know is which method to use to get from the left side to the right side. That is a step non-obvious to me and it has to be.

Homework Statement The initial problem is to calculate \int_{-\infty}^{\infty}\cos(x^{2})dx using t=x^{2} and then t^{-\frac{1}{2}}=\frac{1}{\sqrt{\pi}}\int_{-\infty}^{\infty}e^{-tu^{2}}du Homework Equations The Attempt at a Solution I have, by transformation and use of the...

What you are looking for seems to be the variance of measurements. For the std-deviation of the mean value: s_{m}=\frac{s}{\sqrt{n}}=\sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}} here then holds for n->infinity s_{m}\rightarrow0\; s\rightarrow\sigma with...

that's a trivial problem asked on electrostatics. Yep, you divide it for a ratio.

Why though? The way known to me to diagonalize a symmetric matrix is TAT^-1 = D with orthogonal matrix T. Following is the way I think I've solved it. Taking off from hunt's equation...

Yep. I've got that hint by a friend yesterday night which led me to: \int e^{-\frac{1}{2}<x,T^{-1}TAT^{-1}Tx>-i<k,T^{-1}Tx>}\Rightarrow\int e^{-\frac{1}{2}<Tx,(TAT^{-1}=D)Tx>-i<Tk,Tx>}\Rightarrow\int e^{-\frac{1}{2}<y,Dy>-i<k',y>}d^{n}y by using that TAT^-1 = D , with D-diagonal. defining...

Homework Statement Let A be a real, symmetric positively definite nxn - matrix. f:\mathbb{R}^{n}\rightarrow\mathbb{R}\; s.t\;\vec{x}\rightarrow e^{-\frac{1}{2}<\vec{x},A\vec{x}>} Show that the FT of f is given by: \hat{f}(\vec{k})=\frac{1}{\sqrt{\det...