Recent content by jac7

Thank you so much for your help!

Thank you very much i think I've finally got it! just a quick question though, when you did the integration for \hat{f}(\xi ) what limits did you integrate between? because when i integrate between infinity and -infinity I am not getting the same thing because the exponentials just disappear...

thankyou! but I'm given the Fourier transform of e^{-x^2/2} is there a simple way of manipulating it so that its the transform of e^{-x^2} or would i have to work that out?

iv tried this and I've ended up with \frac{-i\xi}{2}\int{e^{-x^2}e^{-ix\xi}}dx is this right? what do i do next?

integration by part of the transform of exp(-x^2) or integration by parts of exp(-x^2)?

I'm sorry but i can't see where to go next or how it could help! i know how you got that and i can see how its the same as my function, but you've already got it into transform form? but i need the transform of xf(x), i know that the transform of xf(x) is if'(xi) is it anything to do with that?

I don't understand what you've done here, when i subbed it in like you did i got (y/2)\sqrt{2pi}e^{-y^2/2}dy

I've tried it with a=f'(x) b'=sin(nx)/n a'=f''(x) b=-cos(nx)/n^2 and iv got that if f is even then the whole is 0 and if f is odd then the whole thing is -2f'(pi)cos(npi)/n^2 I feel like I've gone wrong here?

i don't know why that's not coming up with f(x)cos(nx) but it is supposed to be there!

I've done it by parts and for my parts I've got u=f(x) v'=cos(nx) u'=f'(x) v=sin(nx)/n so then i get 0-\int\frac{sin(nx)}{n}f'(x)dx (with the integral still between -pi and pi) but then if i do this again with a=sin(nx)/n b'=f'(x) a'=cos(nx) b=f(x) i just end up with...

Thankyou for replying to my question! If cos(-n*pi) = cos(n*pi) does that just mean that the integral becomes 0 to pi because -pi=pi? I'm not quite sure what you mean by using this though because if i integrate cos(nx) it becomes -sin(nx)/n and then this doesn't apply anymore because...

I need to find the Fourier transform to this function and I'm really stuck, because i tried substituting it into the Fourier transform equations but i started to get a really long integral that got out of hand! i also know that but i don't know how to incorporate it into finding the Fourier...

I am so stuck on my revision and i really need someones help! I am using the definition of Fourier series as My lecturer has told us that if f is odd. Could someone please tell me how he has derived this because i can't understand how he's got to it, iv tried using trig identities and...

sorry here is the attachment

I have been given this question (in the attachment). I have a deifnition for what it means for a function to be in the schwartz class, but I don't know how to start showing that the hermite function belongs to it? I have attempted to write out the first couple of terms using the n+1 formula...