Today we talked about section 13-15, the second Bessel function, an aside on Gamma function, the shape of Bessel functions, and some recursion relations.
The explanation from Boas are quite detailed, so I won't repeat it here. A rough outline of the lecture is the following
The shape of $J_p(x)$ is an oscillation damping. Try https://www.wolframalpha.com/, with input
This will tell you something about $J_0(x)$. Change 0 to other number and play with it. The Neumann function $Y_n(x)$ is called 'BesselY[n,x]'. The program will show the real and imaginary part for $x < 0$. For us, one only need to look at $x>0$'s real part.
For recursion relation, we checked the equation (15.2). Basically, one just plug in the general fomula of $J_p(x)$ and simplify.