Recent content by lamarche

Your data looks convincing. I had the wrong intuition. Do you think the function actually reaches zero at some negative value (e.g. -2 ?)? or do you think it is entire? I tried a Taylor expansion on it, and I actually got some hints of an infinite radius of convergence!

Hi! JJ, caution, in English you would say "chance" not "hasard"... "hasard" is like "danger" You are right, I flipped the sign of x in what I sent you (here I actually FFT/IFFT with MATLAB), so on your graph what I call a singularity is at +1.6..., not -1.6... and the impulse response...

Hi! JJ, Cos(a+b) = cos(a) cos(b) - sin(a) sin(b) so actually what you want to plot is (2) minus (3), not plus... which is such that the function abruply goes to zero (and stays exactly there) at -pi^2/6 It is a singularity in the same way that the function f=(0,x<=0;exp(-1/x),x>0)...

https://www.physicsforums.com/showthread.php?p=3025068#post3025068" You're right, I posted my question at the above link

The integral I am seeking to evaluate is int_{-\inf}^{+\inf) exp(-|w|/2) exp( i w [ln(|w|)/pi-x]) dw a definite integral which is a function of x... at x=0, it is nearly the same as the "sophomore dream" integral... I don't know why, but this function seems to have a singularity at...

Hi! JJ, The integral I am seeking to evaluate is int_{-\inf}^{+\inf) exp(-|w|/2) exp( i w [ln(|w|)/pi-x]) dw a definite integral which is a function of x... I don't know why, but this function seems to have a singularity at -pi^2/6 This does have a physical application: it would be...

JJ, You seem to know a lot about this "int x^x" function - does it have poles or zeros on the complex plane? does it have the same branch cuts as x ln(x) (or ln(x)) ?? That's the real importance of creating a new function ... to know the pole/zero/cut structure I am asking because...

I am myself looking for a similar answer. I came to this question while looking for the Fourier transform of causal impulse responses. In what context did you come to yours? I may have an answer for you: the Lambert W funtion may have the solution you are looking for...