# Thread: Help in Finding the Fourier Sine Transform

1. ## Help in Finding the Fourier Sine Transform

I need your help in finding the Fourier Sine Transform of (x^(n-1))

2. ## Re: Help in Finding the Fourier Sine Transform

Two questions:

1. What is your definition of the Fourier Sine Transform? (There are more than one.)
2. What integral are you then supposed to compute?

3. ## Re: Help in Finding the Fourier Sine Transform

My definition.

($\displaystyle \sqrt$ 2/ $\displaystyle \pi$) $\displaystyle \int$ (from 0 to infinity) $\displaystyle x^{n-1}$sinsx.dx

4. ## Re: Help in Finding the Fourier Sine Transform

Just to clarify:

$\displaystyle \mathcal{F}_{s}[x^{n-1}]:=\sqrt{\frac{2}{\pi}}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx.$

Correct? Or is it

$\displaystyle \mathcal{F}_{s}[x^{n-1}]:=\frac{\sqrt{2}}{\pi}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx?$

Assuming one of these forms is correct (I'm guessing the first), what thoughts have you had so far?

5. ## Re: Help in Finding the Fourier Sine Transform

Originally Posted by sunveer
My definition.

($\displaystyle \sqrt$ 2/ $\displaystyle \pi$) $\displaystyle \int$ (from 0 to infinity) $\displaystyle x^{n-1}$sinsx.dx
What are the restrictions on $\displaystyle n$ ?

CB

6. ## Re: Help in Finding the Fourier Sine Transform

The first form is correct. You are right.

Also, there are no restrictions on 'n'

7. ## Re: Help in Finding the Fourier Sine Transform

See here. I don't know if the link I posted will get you the "Allow More Time" option, but you'll need to click that, if it doesn't give you the answer right away. You'll note the restrictions on n in the final result, as well as the restriction on s. Mathematica doesn't give an answer if those restrictions aren't met. I suspect the integral may not actually exist in that situation.