Hello, I am in the process of showing that the modified Bessel function, I_v(x), is a solution to the modified Bessel equation, x^2*y''+x*y'-(x^2+v^2)*y=0 I have differentiated the MBF twice and plugged it in to show that the left hand side is in fact 0. After a good amount of work, I've come to the following left hand side: Where sigma=v. Is that right? The math seems straight forward, and I only did one change of index that looks correct to me. I'm skeptical about the end result though.