Can the Fourier integral of sinw be solved with a misprint?

  • Thread starter Thread starter zezima1
  • Start date Start date
  • Tags Tags
    Fourier Integral
zezima1
Messages
119
Reaction score
0
I'm a little unsure of how the attached solutions are obtained. For instance one of the Fourier integrals is:

∫e(wE-iw)t = [1/(wE-iw)e(wE-iw)t from -∞ to ∞. But what do you do about the real part wE? That leads the integral to diverge as far as I can see...
 

Attachments

  • fouriertransform.png
    fouriertransform.png
    3.9 KB · Views: 393
Physics news on Phys.org
hizezima1! :smile:

those ewEts are a misprint, they should be eiwEt :wink:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Fourier transform ##f(t) = te^{-at}##
Replies
6
Views
3K
Calculate the Fourier transform of the susceptibility of an Oscillator
Replies
1
Views
2K
Fourier Transform - Solutions Error?
Replies
5
Views
1K
Fourier transform of wave packet
Replies
3
Views
1K
Solve integral by finding Fourier series of complex function
Replies
3
Views
1K
A few questions to make sure I understand Fourier series
Replies
3
Views
2K
Why only odd cosine terms in this Fourier series?
Replies
1
Views
1K
Finding the Fourier cosine series for ##f(x)=x^2##
Replies
4
Views
2K
Characterize Fourier coefficients
Replies
2
Views
2K
Why is the Fourier coefficent calculated like this?
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top