Recent content by youth4ever

@Random Variable Thanks again. How you would approach a problem like the following : It come from the Fourier transform of the sinc function without the coefficient. $$ \int_{0}^{\infty} \frac{sin (ak)}{ak} e^{ikx} \ dk $$ Without the exponential term hanged there that would be easy and is...

Hello "Random Variable" And many thanks for the solution. Your solution is incredible. I am amazed. I have a question although. How you knew at this point $$ = \int_{0}^{\infty} \frac{1}{a^{2}+x^{2}} \frac{s}{s^{2}+(mx)^{2}} \ dx $$ to amplify the product with...

Hi Opalg, Yes I know that it comes from e^imx/... integral. But I wondered if there is a way to simply integrate the cosine part separately by using a different technique and to double check the answer. Is this possible ? Thanks.

Hello my Math friends, I have a complex integration problem: The integral to calculate is : Integrate[Cos [mx]/(x^2 + a^2), {x, -Infinity, Infinity}] or if particularized for a=1, m=1 the integral will be : Integrate[Cos [x]/(x^2 + 1), {x, -Infinity, Infinity}] I know the answer for both of...

I like very much Euler. Imagine how limited mathematics would be without the Euler formula. I remained impressed for the rest of my life when I saw how he solved the famous limit $$Sum from 0 to Infinity 1/x^2$$ A Famous Infinite Series