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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.

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# Showing That the Modified Bessel Function of the First Kind is a Solution

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