Well I did post this in the maths section. Could you elaborate particularly what the point of orthogonality of Fourier series and Sturm-Liouville problems implies?
I understand that a function is orthogonal if the inner product of any two functions of an infinite series equal to zero.
My question is why do we prove functions are orthogonal? What can we do with this information?
QUESTION:
The question is to find the improper integral of (x^1/2)/lnx dx.
MY ATTEMPT:
1)I tried it byparts, by taking 1/ln x as 'u' or the first function but i got stuck.
2)Alternatively, I tried substituting x=e^2t in hopes to eliminate ln for a simpler byparts integration, but that didn't...