have a look at attachment :
I have been trying to replicate a result given in a textbook that says
where is the Bessel Function of the First Kind.
Can someone show me how to get this from the recurrence formulae for Bessel derivatives found in the literature as
My problem was in using the recurrence formulae for the case m=2. Not sure how to interpret (d/dx)^2, but your way avoids this.